exp_30_runs_two_attr – Complete Experiment Report
Vary_Correlation_with_high_Dimension
(MvNormal,
correlation,
30 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-7.575 |
3.47e-10 |
-1.843 |
| HMC |
0.3 |
2.309 |
0.0258 |
0.940 |
| HMC |
0.5 |
4.277 |
0.000146 |
2.778 |
| HMC |
0.9 |
6.108 |
7.09e-07 |
4.421 |
| HMC |
0.99 |
6.064 |
1.14e-06 |
7.808 |
| SMC |
0.0 |
-0.395 |
0.694 |
-0.101 |
| SMC |
0.3 |
-0.054 |
0.958 |
-0.012 |
| SMC |
0.5 |
1.462 |
0.149 |
0.404 |
| SMC |
0.9 |
-0.024 |
0.981 |
-0.006 |
| SMC |
0.99 |
1.160 |
0.251 |
0.326 |
| Metro |
0.0 |
14.074 |
6.54e-19 |
4.761 |
| Metro |
0.3 |
6.690 |
2.03e-07 |
8.959 |
| Metro |
0.5 |
5.331 |
9.52e-06 |
9.594 |
| Metro |
0.9 |
7.114 |
7.6e-08 |
21.662 |
| Metro |
0.99 |
7.518 |
2.74e-08 |
65.387 |
| DEMetro_Z |
0.0 |
41.477 |
2.25e-27 |
2215.116 |
| DEMetro_Z |
0.3 |
40.550 |
4.28e-27 |
1128.335 |
| DEMetro_Z |
0.5 |
39.997 |
6.32e-27 |
878.867 |
| DEMetro_Z |
0.9 |
41.384 |
2.36e-27 |
510.899 |
| DEMetro_Z |
0.99 |
41.240 |
2.6e-27 |
465.804 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0.0
|
-41.545
|
2.15e-27
|
-7.585
|
| HMC_vs_DEMetro_Z |
0.3
|
-40.514
|
4.41e-27
|
-7.397
|
| HMC_vs_DEMetro_Z |
0.5
|
-40.089
|
5.96e-27
|
-7.319
|
| HMC_vs_DEMetro_Z |
0.9
|
-41.591
|
2.09e-27
|
-7.593
|
| HMC_vs_DEMetro_Z |
0.99
|
-41.046
|
3.04e-27
|
-7.494
|
| Metro_vs_SMC |
0.0
|
13.370
|
6.27e-14
|
2.441
|
| Metro_vs_SMC |
0.3
|
6.884
|
1.46e-07
|
1.257
|
| Metro_vs_SMC |
0.5
|
4.975
|
2.72e-05
|
0.908
|
| Metro_vs_SMC |
0.9
|
7.177
|
6.71e-08
|
1.310
|
| Metro_vs_SMC |
0.99
|
7.449
|
3.29e-08
|
1.360
|
| Metro_vs_DEMetro_Z |
0.0
|
-41.366
|
2.44e-27
|
-7.552
|
| Metro_vs_DEMetro_Z |
0.3
|
-40.989
|
3.16e-27
|
-7.483
|
| Metro_vs_DEMetro_Z |
0.5
|
-39.241
|
1.1e-26
|
-7.164
|
| Metro_vs_DEMetro_Z |
0.9
|
-38.624
|
1.72e-26
|
-7.052
|
| Metro_vs_DEMetro_Z |
0.99
|
-28.206
|
1.24e-22
|
-5.150
|
| HMC_vs_Metro |
0.0
|
-19.778
|
2.22e-18
|
-3.611
|
| HMC_vs_Metro |
0.3
|
-5.533
|
5.77e-06
|
-1.010
|
| HMC_vs_Metro |
0.5
|
-3.614
|
0.00113
|
-0.660
|
| HMC_vs_Metro |
0.9
|
-5.533
|
5.78e-06
|
-1.010
|
| HMC_vs_Metro |
0.99
|
-6.416
|
5.13e-07
|
-1.171
|
| HMC_vs_SMC |
0.0
|
-9.093
|
5.46e-10
|
-1.660
|
| HMC_vs_SMC |
0.3
|
2.281
|
0.0301
|
0.416
|
| HMC_vs_SMC |
0.5
|
4.070
|
0.000331
|
0.743
|
| HMC_vs_SMC |
0.9
|
6.059
|
1.36e-06
|
1.106
|
| HMC_vs_SMC |
0.99
|
6.038
|
1.44e-06
|
1.102
|
| DEMetro_Z_vs_SMC |
0.0
|
41.451
|
2.3e-27
|
7.568
|
| DEMetro_Z_vs_SMC |
0.3
|
40.516
|
4.41e-27
|
7.397
|
| DEMetro_Z_vs_SMC |
0.5
|
40.104
|
5.9e-27
|
7.322
|
| DEMetro_Z_vs_SMC |
0.9
|
41.406
|
2.37e-27
|
7.560
|
| DEMetro_Z_vs_SMC |
0.99
|
41.183
|
2.76e-27
|
7.519
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.018 |
0.023 |
0.003 |
-1.843 |
| HMC |
0.3 |
0.028 |
0.023 |
0.006 |
0.940 |
| HMC |
0.5 |
0.042 |
0.021 |
0.008 |
2.778 |
| HMC |
0.9 |
0.079 |
0.019 |
0.013 |
4.421 |
| HMC |
0.99 |
0.119 |
0.019 |
0.013 |
7.808 |
| SMC |
0.0 |
0.023 |
0.023 |
0.003 |
-0.101 |
| SMC |
0.3 |
0.023 |
0.023 |
0.006 |
-0.012 |
| SMC |
0.5 |
0.024 |
0.021 |
0.008 |
0.404 |
| SMC |
0.9 |
0.019 |
0.019 |
0.013 |
-0.006 |
| SMC |
0.99 |
0.023 |
0.019 |
0.013 |
0.326 |
| Metro |
0.0 |
0.037 |
0.023 |
0.003 |
4.761 |
| Metro |
0.3 |
0.076 |
0.023 |
0.006 |
8.959 |
| Metro |
0.5 |
0.094 |
0.021 |
0.008 |
9.594 |
| Metro |
0.9 |
0.310 |
0.019 |
0.013 |
21.662 |
| Metro |
0.99 |
0.858 |
0.019 |
0.013 |
65.387 |
| DEMetro_Z |
0.0 |
6.543 |
0.023 |
0.003 |
2215.116 |
| DEMetro_Z |
0.3 |
6.762 |
0.023 |
0.006 |
1128.335 |
| DEMetro_Z |
0.5 |
6.672 |
0.021 |
0.008 |
878.867 |
| DEMetro_Z |
0.9 |
6.870 |
0.019 |
0.013 |
510.899 |
| DEMetro_Z |
0.99 |
5.991 |
0.019 |
0.013 |
465.804 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
8.416 |
5.25e-11 |
2.951 |
| HMC |
0.3 |
5.135 |
3.76e-06 |
1.496 |
| HMC |
0.5 |
2.801 |
0.00826 |
1.686 |
| HMC |
0.9 |
4.935 |
2.85e-05 |
7.665 |
| HMC |
0.99 |
5.353 |
8.31e-06 |
6.476 |
| SMC |
0.0 |
3.182 |
0.00245 |
0.997 |
| SMC |
0.3 |
1.999 |
0.0512 |
0.680 |
| SMC |
0.5 |
2.734 |
0.00868 |
0.935 |
| SMC |
0.9 |
2.246 |
0.0301 |
0.955 |
| SMC |
0.99 |
-1.420 |
0.161 |
-0.388 |
| Metro |
0.0 |
14.662 |
2.18e-18 |
5.870 |
| Metro |
0.3 |
10.248 |
1.29e-11 |
8.570 |
| Metro |
0.5 |
7.823 |
1.06e-08 |
13.085 |
| Metro |
0.9 |
6.405 |
5.19e-07 |
27.776 |
| Metro |
0.99 |
5.108 |
1.88e-05 |
117.039 |
| DEMetro_Z |
0.0 |
31.296 |
6.68e-24 |
46855.551 |
| DEMetro_Z |
0.3 |
35.735 |
1.57e-25 |
42367.030 |
| DEMetro_Z |
0.5 |
43.085 |
7.62e-28 |
34672.650 |
| DEMetro_Z |
0.9 |
40.696 |
3.88e-27 |
19905.158 |
| DEMetro_Z |
0.99 |
35.603 |
1.74e-25 |
8465.852 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0.0
|
6.923
|
1.31e-07
|
1.264
|
| HMC_vs_SMC |
0.3
|
2.222
|
0.0342
|
0.406
|
| HMC_vs_SMC |
0.5
|
1.176
|
0.249
|
0.215
|
| HMC_vs_SMC |
0.9
|
4.054
|
0.000346
|
0.740
|
| HMC_vs_SMC |
0.99
|
5.567
|
5.25e-06
|
1.016
|
| Metro_vs_DEMetro_Z |
0.0
|
-31.293
|
6.7e-24
|
-5.713
|
| Metro_vs_DEMetro_Z |
0.3
|
-35.739
|
1.56e-25
|
-6.525
|
| Metro_vs_DEMetro_Z |
0.5
|
-43.057
|
7.76e-28
|
-7.861
|
| Metro_vs_DEMetro_Z |
0.9
|
-40.622
|
4.09e-27
|
-7.416
|
| Metro_vs_DEMetro_Z |
0.99
|
-34.621
|
3.85e-25
|
-6.321
|
| HMC_vs_Metro |
0.0
|
-7.905
|
1.02e-08
|
-1.443
|
| HMC_vs_Metro |
0.3
|
-7.957
|
8.93e-09
|
-1.453
|
| HMC_vs_Metro |
0.5
|
-6.999
|
1.07e-07
|
-1.278
|
| HMC_vs_Metro |
0.9
|
-4.369
|
0.000146
|
-0.798
|
| HMC_vs_Metro |
0.99
|
-4.824
|
4.13e-05
|
-0.881
|
| HMC_vs_DEMetro_Z |
0.0
|
-31.294
|
6.69e-24
|
-5.714
|
| HMC_vs_DEMetro_Z |
0.3
|
-35.735
|
1.57e-25
|
-6.524
|
| HMC_vs_DEMetro_Z |
0.5
|
-43.078
|
7.65e-28
|
-7.865
|
| HMC_vs_DEMetro_Z |
0.9
|
-40.685
|
3.91e-27
|
-7.428
|
| HMC_vs_DEMetro_Z |
0.99
|
-35.575
|
1.78e-25
|
-6.495
|
| Metro_vs_SMC |
0.0
|
12.158
|
6.59e-13
|
2.220
|
| Metro_vs_SMC |
0.3
|
9.767
|
1.12e-10
|
1.783
|
| Metro_vs_SMC |
0.5
|
7.104
|
8.13e-08
|
1.297
|
| Metro_vs_SMC |
0.9
|
5.916
|
2.01e-06
|
1.080
|
| Metro_vs_SMC |
0.99
|
5.118
|
1.83e-05
|
0.934
|
| DEMetro_Z_vs_SMC |
0.0
|
31.295
|
6.69e-24
|
5.714
|
| DEMetro_Z_vs_SMC |
0.3
|
35.737
|
1.56e-25
|
6.525
|
| DEMetro_Z_vs_SMC |
0.5
|
43.083
|
7.63e-28
|
7.866
|
| DEMetro_Z_vs_SMC |
0.9
|
40.692
|
3.89e-27
|
7.429
|
| DEMetro_Z_vs_SMC |
0.99
|
35.609
|
1.73e-25
|
6.501
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.042 |
0.032 |
0.004 |
2.951 |
| HMC |
0.3 |
0.037 |
0.031 |
0.004 |
1.496 |
| HMC |
0.5 |
0.039 |
0.030 |
0.005 |
1.686 |
| HMC |
0.9 |
0.095 |
0.024 |
0.009 |
7.665 |
| HMC |
0.99 |
0.154 |
0.034 |
0.018 |
6.476 |
| SMC |
0.0 |
0.035 |
0.032 |
0.004 |
0.997 |
| SMC |
0.3 |
0.034 |
0.031 |
0.004 |
0.680 |
| SMC |
0.5 |
0.035 |
0.030 |
0.005 |
0.935 |
| SMC |
0.9 |
0.033 |
0.024 |
0.009 |
0.955 |
| SMC |
0.99 |
0.027 |
0.034 |
0.018 |
-0.388 |
| Metro |
0.0 |
0.052 |
0.032 |
0.004 |
5.870 |
| Metro |
0.3 |
0.068 |
0.031 |
0.004 |
8.570 |
| Metro |
0.5 |
0.099 |
0.030 |
0.005 |
13.085 |
| Metro |
0.9 |
0.282 |
0.024 |
0.009 |
27.776 |
| Metro |
0.99 |
2.198 |
0.034 |
0.018 |
117.039 |
| DEMetro_Z |
0.0 |
166.178 |
0.032 |
0.004 |
46855.551 |
| DEMetro_Z |
0.3 |
183.099 |
0.031 |
0.004 |
42367.030 |
| DEMetro_Z |
0.5 |
181.841 |
0.030 |
0.005 |
34672.650 |
| DEMetro_Z |
0.9 |
184.755 |
0.024 |
0.009 |
19905.158 |
| DEMetro_Z |
0.99 |
156.561 |
0.034 |
0.018 |
8465.852 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-2.475 |
0.0163 |
-0.604 |
| HMC |
0.3 |
3.416 |
0.00144 |
1.461 |
| HMC |
0.5 |
4.469 |
9.19e-05 |
3.624 |
| HMC |
0.9 |
7.218 |
4.11e-08 |
7.320 |
| HMC |
0.99 |
9.176 |
3.24e-10 |
12.746 |
| SMC |
0.0 |
0.139 |
0.89 |
0.036 |
| SMC |
0.3 |
0.188 |
0.851 |
0.041 |
| SMC |
0.5 |
1.812 |
0.0754 |
0.514 |
| SMC |
0.9 |
0.627 |
0.533 |
0.159 |
| SMC |
0.99 |
1.402 |
0.166 |
0.374 |
| Metro |
0.0 |
15.833 |
5.86e-20 |
6.055 |
| Metro |
0.3 |
7.773 |
1.19e-08 |
12.413 |
| Metro |
0.5 |
5.989 |
1.57e-06 |
14.394 |
| Metro |
0.9 |
9.800 |
9.89e-11 |
35.751 |
| Metro |
0.99 |
11.973 |
9.49e-13 |
120.398 |
| DEMetro_Z |
0.0 |
61.863 |
2.37e-32 |
5860.936 |
| DEMetro_Z |
0.3 |
69.837 |
7.18e-34 |
3153.652 |
| DEMetro_Z |
0.5 |
92.846 |
1.92e-37 |
2450.664 |
| DEMetro_Z |
0.9 |
96.813 |
5.65e-38 |
1461.432 |
| DEMetro_Z |
0.99 |
68.671 |
1.15e-33 |
1199.616 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0.0
|
-61.721
|
2.53e-32
|
-11.269
|
| Metro_vs_DEMetro_Z |
0.3
|
-69.683
|
7.67e-34
|
-12.722
|
| Metro_vs_DEMetro_Z |
0.5
|
-88.338
|
8.14e-37
|
-16.128
|
| Metro_vs_DEMetro_Z |
0.9
|
-89.771
|
5.12e-37
|
-16.390
|
| Metro_vs_DEMetro_Z |
0.99
|
-56.031
|
4.09e-31
|
-10.230
|
| DEMetro_Z_vs_SMC |
0.0
|
61.832
|
2.4e-32
|
11.289
|
| DEMetro_Z_vs_SMC |
0.3
|
69.861
|
7.13e-34
|
12.755
|
| DEMetro_Z_vs_SMC |
0.5
|
93.032
|
1.82e-37
|
16.985
|
| DEMetro_Z_vs_SMC |
0.9
|
96.886
|
5.64e-38
|
17.689
|
| DEMetro_Z_vs_SMC |
0.99
|
68.604
|
1.2e-33
|
12.525
|
| HMC_vs_DEMetro_Z |
0.0
|
-61.880
|
2.35e-32
|
-11.298
|
| HMC_vs_DEMetro_Z |
0.3
|
-69.850
|
7.16e-34
|
-12.753
|
| HMC_vs_DEMetro_Z |
0.5
|
-93.028
|
1.83e-37
|
-16.985
|
| HMC_vs_DEMetro_Z |
0.9
|
-96.357
|
6.61e-38
|
-17.592
|
| HMC_vs_DEMetro_Z |
0.99
|
-69.192
|
9.4e-34
|
-12.633
|
| HMC_vs_Metro |
0.0
|
-17.042
|
1.2e-16
|
-3.111
|
| HMC_vs_Metro |
0.3
|
-6.391
|
5.48e-07
|
-1.167
|
| HMC_vs_Metro |
0.5
|
-4.277
|
0.000188
|
-0.781
|
| HMC_vs_Metro |
0.9
|
-7.503
|
2.86e-08
|
-1.370
|
| HMC_vs_Metro |
0.99
|
-10.193
|
4.27e-11
|
-1.861
|
| HMC_vs_SMC |
0.0
|
-3.178
|
0.00351
|
-0.580
|
| HMC_vs_SMC |
0.3
|
3.272
|
0.00276
|
0.597
|
| HMC_vs_SMC |
0.5
|
4.239
|
0.000209
|
0.774
|
| HMC_vs_SMC |
0.9
|
6.886
|
1.45e-07
|
1.257
|
| HMC_vs_SMC |
0.99
|
9.354
|
2.94e-10
|
1.708
|
| Metro_vs_SMC |
0.0
|
13.958
|
2.12e-14
|
2.548
|
| Metro_vs_SMC |
0.3
|
7.854
|
1.16e-08
|
1.434
|
| Metro_vs_SMC |
0.5
|
5.655
|
4.12e-06
|
1.033
|
| Metro_vs_SMC |
0.9
|
9.836
|
9.59e-11
|
1.796
|
| Metro_vs_SMC |
0.99
|
11.875
|
1.17e-12
|
2.168
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.028 |
0.029 |
0.002 |
-0.604 |
| HMC |
0.3 |
0.034 |
0.029 |
0.003 |
1.461 |
| HMC |
0.5 |
0.043 |
0.027 |
0.004 |
3.624 |
| HMC |
0.9 |
0.079 |
0.024 |
0.007 |
7.320 |
| HMC |
0.99 |
0.127 |
0.024 |
0.008 |
12.746 |
| SMC |
0.0 |
0.029 |
0.029 |
0.002 |
0.036 |
| SMC |
0.3 |
0.029 |
0.029 |
0.003 |
0.041 |
| SMC |
0.5 |
0.029 |
0.027 |
0.004 |
0.514 |
| SMC |
0.9 |
0.025 |
0.024 |
0.007 |
0.159 |
| SMC |
0.99 |
0.027 |
0.024 |
0.008 |
0.374 |
| Metro |
0.0 |
0.040 |
0.029 |
0.002 |
6.055 |
| Metro |
0.3 |
0.070 |
0.029 |
0.003 |
12.413 |
| Metro |
0.5 |
0.089 |
0.027 |
0.004 |
14.394 |
| Metro |
0.9 |
0.290 |
0.024 |
0.007 |
35.751 |
| Metro |
0.99 |
0.994 |
0.024 |
0.008 |
120.398 |
| DEMetro_Z |
0.0 |
10.069 |
0.029 |
0.002 |
5860.936 |
| DEMetro_Z |
0.3 |
10.515 |
0.029 |
0.003 |
3153.652 |
| DEMetro_Z |
0.5 |
10.599 |
0.027 |
0.004 |
2450.664 |
| DEMetro_Z |
0.9 |
10.870 |
0.024 |
0.007 |
1461.432 |
| DEMetro_Z |
0.99 |
9.683 |
0.024 |
0.008 |
1199.616 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-3.952 |
0.000234 |
-0.884 |
| HMC |
0.3 |
3.081 |
0.00363 |
1.277 |
| HMC |
0.5 |
4.484 |
8.52e-05 |
3.364 |
| HMC |
0.9 |
6.884 |
1.09e-07 |
7.602 |
| HMC |
0.99 |
8.385 |
2.24e-09 |
10.996 |
| SMC |
0.0 |
0.914 |
0.365 |
0.219 |
| SMC |
0.3 |
0.965 |
0.339 |
0.222 |
| SMC |
0.5 |
2.236 |
0.0293 |
0.622 |
| SMC |
0.9 |
1.177 |
0.244 |
0.342 |
| SMC |
0.99 |
0.587 |
0.559 |
0.155 |
| Metro |
0.0 |
14.499 |
7.44e-20 |
4.640 |
| Metro |
0.3 |
8.609 |
1.31e-09 |
11.767 |
| Metro |
0.5 |
6.843 |
1.52e-07 |
15.474 |
| Metro |
0.9 |
9.538 |
1.82e-10 |
35.948 |
| Metro |
0.99 |
15.669 |
1.03e-15 |
80.319 |
| DEMetro_Z |
0.0 |
97.693 |
2.92e-38 |
326.961 |
| DEMetro_Z |
0.3 |
85.705 |
1.04e-36 |
227.241 |
| DEMetro_Z |
0.5 |
93.201 |
6.43e-38 |
201.167 |
| DEMetro_Z |
0.9 |
90.416 |
2.51e-38 |
115.739 |
| DEMetro_Z |
0.99 |
97.440 |
2.66e-40 |
93.676 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0.0
|
99.156
|
2.89e-38
|
18.103
|
| DEMetro_Z_vs_SMC |
0.3
|
85.209
|
2.31e-36
|
15.557
|
| DEMetro_Z_vs_SMC |
0.5
|
93.198
|
1.73e-37
|
17.016
|
| DEMetro_Z_vs_SMC |
0.9
|
91.710
|
2.76e-37
|
16.744
|
| DEMetro_Z_vs_SMC |
0.99
|
95.164
|
9.48e-38
|
17.374
|
| HMC_vs_Metro |
0.0
|
-18.516
|
1.31e-17
|
-3.381
|
| HMC_vs_Metro |
0.3
|
-7.011
|
1.04e-07
|
-1.280
|
| HMC_vs_Metro |
0.5
|
-5.144
|
1.7e-05
|
-0.939
|
| HMC_vs_Metro |
0.9
|
-7.146
|
7.27e-08
|
-1.305
|
| HMC_vs_Metro |
0.99
|
-13.011
|
1.24e-13
|
-2.375
|
| Metro_vs_DEMetro_Z |
0.0
|
-96.141
|
7.05e-38
|
-17.553
|
| Metro_vs_DEMetro_Z |
0.3
|
-78.932
|
2.1e-35
|
-14.411
|
| Metro_vs_DEMetro_Z |
0.5
|
-58.911
|
9.67e-32
|
-10.756
|
| Metro_vs_DEMetro_Z |
0.9
|
-21.550
|
2.15e-19
|
-3.935
|
| Metro_vs_DEMetro_Z |
0.99
|
-2.621
|
0.0138
|
-0.478
|
| HMC_vs_SMC |
0.0
|
-6.617
|
2.98e-07
|
-1.208
|
| HMC_vs_SMC |
0.3
|
2.574
|
0.0154
|
0.470
|
| HMC_vs_SMC |
0.5
|
4.181
|
0.000245
|
0.763
|
| HMC_vs_SMC |
0.9
|
6.462
|
4.52e-07
|
1.180
|
| HMC_vs_SMC |
0.99
|
8.385
|
3.05e-09
|
1.531
|
| Metro_vs_SMC |
0.0
|
13.369
|
6.28e-14
|
2.441
|
| Metro_vs_SMC |
0.3
|
8.492
|
2.34e-09
|
1.550
|
| Metro_vs_SMC |
0.5
|
6.416
|
5.12e-07
|
1.171
|
| Metro_vs_SMC |
0.9
|
9.423
|
2.5e-10
|
1.720
|
| Metro_vs_SMC |
0.99
|
15.640
|
1.14e-15
|
2.855
|
| HMC_vs_DEMetro_Z |
0.0
|
-99.031
|
3e-38
|
-18.080
|
| HMC_vs_DEMetro_Z |
0.3
|
-84.604
|
2.84e-36
|
-15.447
|
| HMC_vs_DEMetro_Z |
0.5
|
-91.946
|
2.56e-37
|
-16.787
|
| HMC_vs_DEMetro_Z |
0.9
|
-66.179
|
3.39e-33
|
-12.083
|
| HMC_vs_DEMetro_Z |
0.99
|
-58.270
|
1.32e-31
|
-10.639
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.013 |
0.014 |
0.002 |
-0.884 |
| HMC |
0.3 |
0.018 |
0.015 |
0.002 |
1.277 |
| HMC |
0.5 |
0.024 |
0.014 |
0.003 |
3.364 |
| HMC |
0.9 |
0.050 |
0.014 |
0.005 |
7.602 |
| HMC |
0.99 |
0.079 |
0.015 |
0.006 |
10.996 |
| SMC |
0.0 |
0.015 |
0.014 |
0.002 |
0.219 |
| SMC |
0.3 |
0.015 |
0.015 |
0.002 |
0.222 |
| SMC |
0.5 |
0.016 |
0.014 |
0.003 |
0.622 |
| SMC |
0.9 |
0.015 |
0.014 |
0.005 |
0.342 |
| SMC |
0.99 |
0.016 |
0.015 |
0.006 |
0.155 |
| Metro |
0.0 |
0.022 |
0.014 |
0.002 |
4.640 |
| Metro |
0.3 |
0.044 |
0.015 |
0.002 |
11.767 |
| Metro |
0.5 |
0.057 |
0.014 |
0.003 |
15.474 |
| Metro |
0.9 |
0.185 |
0.014 |
0.005 |
35.948 |
| Metro |
0.99 |
0.485 |
0.015 |
0.006 |
80.319 |
| DEMetro_Z |
0.0 |
0.570 |
0.014 |
0.002 |
326.961 |
| DEMetro_Z |
0.3 |
0.578 |
0.015 |
0.002 |
227.241 |
| DEMetro_Z |
0.5 |
0.575 |
0.014 |
0.003 |
201.167 |
| DEMetro_Z |
0.9 |
0.566 |
0.014 |
0.005 |
115.739 |
| DEMetro_Z |
0.99 |
0.564 |
0.015 |
0.006 |
93.676 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-7.841 |
1.82e-10 |
-1.790 |
| HMC |
0.3 |
1.702 |
0.0959 |
0.682 |
| HMC |
0.5 |
3.656 |
0.000862 |
2.418 |
| HMC |
0.9 |
4.841 |
3.32e-05 |
4.585 |
| HMC |
0.99 |
4.552 |
8.52e-05 |
9.191 |
| SMC |
0.0 |
-0.459 |
0.648 |
-0.124 |
| SMC |
0.3 |
0.947 |
0.348 |
0.270 |
| SMC |
0.5 |
0.513 |
0.61 |
0.132 |
| SMC |
0.9 |
-0.424 |
0.673 |
-0.096 |
| SMC |
0.99 |
0.458 |
0.649 |
0.138 |
| Metro |
0.0 |
15.213 |
1.33e-20 |
4.945 |
| Metro |
0.3 |
6.912 |
9.84e-08 |
7.330 |
| Metro |
0.5 |
6.585 |
2.93e-07 |
11.766 |
| Metro |
0.9 |
7.971 |
8.48e-09 |
43.089 |
| Metro |
0.99 |
6.634 |
2.84e-07 |
109.335 |
| DEMetro_Z |
0.0 |
21.905 |
1.37e-19 |
3704.994 |
| DEMetro_Z |
0.3 |
45.126 |
2.03e-28 |
1972.704 |
| DEMetro_Z |
0.5 |
35.886 |
1.39e-25 |
1563.810 |
| DEMetro_Z |
0.9 |
43.628 |
5.29e-28 |
900.256 |
| DEMetro_Z |
0.99 |
31.470 |
5.69e-24 |
764.866 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0.0
|
-21.914
|
1.36e-19
|
-4.001
|
| HMC_vs_DEMetro_Z |
0.3
|
-45.247
|
1.88e-28
|
-8.261
|
| HMC_vs_DEMetro_Z |
0.5
|
-35.738
|
1.56e-25
|
-6.525
|
| HMC_vs_DEMetro_Z |
0.9
|
-43.710
|
5.05e-28
|
-7.980
|
| HMC_vs_DEMetro_Z |
0.99
|
-31.586
|
5.15e-24
|
-5.767
|
| Metro_vs_SMC |
0.0
|
16.637
|
2.26e-16
|
3.037
|
| Metro_vs_SMC |
0.3
|
6.330
|
6.48e-07
|
1.156
|
| Metro_vs_SMC |
0.5
|
6.724
|
2.23e-07
|
1.228
|
| Metro_vs_SMC |
0.9
|
7.996
|
8.09e-09
|
1.460
|
| Metro_vs_SMC |
0.99
|
6.589
|
3.21e-07
|
1.203
|
| Metro_vs_DEMetro_Z |
0.0
|
-21.882
|
1.42e-19
|
-3.995
|
| Metro_vs_DEMetro_Z |
0.3
|
-44.829
|
2.45e-28
|
-8.185
|
| Metro_vs_DEMetro_Z |
0.5
|
-35.967
|
1.3e-25
|
-6.567
|
| Metro_vs_DEMetro_Z |
0.9
|
-44.248
|
3.56e-28
|
-8.079
|
| Metro_vs_DEMetro_Z |
0.99
|
-23.154
|
3e-20
|
-4.227
|
| HMC_vs_Metro |
0.0
|
-22.948
|
3.83e-20
|
-4.190
|
| HMC_vs_Metro |
0.3
|
-5.710
|
3.54e-06
|
-1.043
|
| HMC_vs_Metro |
0.5
|
-4.640
|
6.89e-05
|
-0.847
|
| HMC_vs_Metro |
0.9
|
-7.069
|
8.92e-08
|
-1.291
|
| HMC_vs_Metro |
0.99
|
-6.330
|
6.47e-07
|
-1.156
|
| HMC_vs_SMC |
0.0
|
-8.069
|
6.74e-09
|
-1.473
|
| HMC_vs_SMC |
0.3
|
1.055
|
0.3
|
0.193
|
| HMC_vs_SMC |
0.5
|
3.418
|
0.00189
|
0.624
|
| HMC_vs_SMC |
0.9
|
5.100
|
1.92e-05
|
0.931
|
| HMC_vs_SMC |
0.99
|
4.279
|
0.000187
|
0.781
|
| DEMetro_Z_vs_SMC |
0.0
|
21.913
|
1.36e-19
|
4.001
|
| DEMetro_Z_vs_SMC |
0.3
|
45.173
|
1.97e-28
|
8.247
|
| DEMetro_Z_vs_SMC |
0.5
|
35.849
|
1.43e-25
|
6.545
|
| DEMetro_Z_vs_SMC |
0.9
|
43.621
|
5.35e-28
|
7.964
|
| DEMetro_Z_vs_SMC |
0.99
|
31.390
|
6.14e-24
|
5.731
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.018 |
0.023 |
0.003 |
-1.790 |
| HMC |
0.3 |
0.027 |
0.023 |
0.006 |
0.682 |
| HMC |
0.5 |
0.039 |
0.021 |
0.008 |
2.418 |
| HMC |
0.9 |
0.081 |
0.019 |
0.013 |
4.585 |
| HMC |
0.99 |
0.137 |
0.019 |
0.013 |
9.191 |
| SMC |
0.0 |
0.023 |
0.023 |
0.003 |
-0.124 |
| SMC |
0.3 |
0.024 |
0.023 |
0.006 |
0.270 |
| SMC |
0.5 |
0.022 |
0.021 |
0.008 |
0.132 |
| SMC |
0.9 |
0.018 |
0.019 |
0.013 |
-0.096 |
| SMC |
0.99 |
0.021 |
0.019 |
0.013 |
0.138 |
| Metro |
0.0 |
0.038 |
0.023 |
0.003 |
4.945 |
| Metro |
0.3 |
0.066 |
0.023 |
0.006 |
7.330 |
| Metro |
0.5 |
0.110 |
0.021 |
0.008 |
11.766 |
| Metro |
0.9 |
0.597 |
0.019 |
0.013 |
43.089 |
| Metro |
0.99 |
1.421 |
0.019 |
0.013 |
109.335 |
| DEMetro_Z |
0.0 |
10.928 |
0.023 |
0.003 |
3704.994 |
| DEMetro_Z |
0.3 |
11.805 |
0.023 |
0.006 |
1972.704 |
| DEMetro_Z |
0.5 |
11.855 |
0.021 |
0.008 |
1563.810 |
| DEMetro_Z |
0.9 |
12.091 |
0.019 |
0.013 |
900.256 |
| DEMetro_Z |
0.99 |
9.825 |
0.019 |
0.013 |
764.866 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
9.591 |
5.51e-13 |
3.139 |
| HMC |
0.3 |
4.906 |
1.11e-05 |
1.719 |
| HMC |
0.5 |
3.691 |
0.000637 |
1.538 |
| HMC |
0.9 |
3.640 |
0.00104 |
9.526 |
| HMC |
0.99 |
5.735 |
2.72e-06 |
6.295 |
| SMC |
0.0 |
-0.381 |
0.705 |
-0.110 |
| SMC |
0.3 |
1.336 |
0.187 |
0.403 |
| SMC |
0.5 |
1.099 |
0.276 |
0.323 |
| SMC |
0.9 |
0.888 |
0.379 |
0.329 |
| SMC |
0.99 |
-1.903 |
0.0621 |
-0.537 |
| Metro |
0.0 |
13.549 |
1.84e-16 |
6.193 |
| Metro |
0.3 |
11.987 |
8.29e-14 |
7.563 |
| Metro |
0.5 |
7.720 |
1.33e-08 |
11.358 |
| Metro |
0.9 |
7.021 |
1e-07 |
38.864 |
| Metro |
0.99 |
38.591 |
1.68e-27 |
43.333 |
| DEMetro_Z |
0.0 |
16.216 |
4.42e-16 |
6154.027 |
| DEMetro_Z |
0.3 |
15.300 |
2.01e-15 |
4299.505 |
| DEMetro_Z |
0.5 |
15.921 |
7.15e-16 |
4034.718 |
| DEMetro_Z |
0.9 |
13.642 |
3.78e-14 |
2424.092 |
| DEMetro_Z |
0.99 |
13.071 |
1.11e-13 |
1241.396 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0.0
|
10.128
|
4.95e-11
|
1.849
|
| HMC_vs_SMC |
0.3
|
3.948
|
0.000461
|
0.721
|
| HMC_vs_SMC |
0.5
|
2.513
|
0.0178
|
0.459
|
| HMC_vs_SMC |
0.9
|
3.502
|
0.00151
|
0.639
|
| HMC_vs_SMC |
0.99
|
6.145
|
1.07e-06
|
1.122
|
| Metro_vs_DEMetro_Z |
0.0
|
-16.201
|
4.53e-16
|
-2.958
|
| Metro_vs_DEMetro_Z |
0.3
|
-15.279
|
2.09e-15
|
-2.790
|
| Metro_vs_DEMetro_Z |
0.5
|
-15.867
|
7.82e-16
|
-2.897
|
| Metro_vs_DEMetro_Z |
0.9
|
-13.435
|
5.55e-14
|
-2.453
|
| Metro_vs_DEMetro_Z |
0.99
|
-12.610
|
2.69e-13
|
-2.302
|
| HMC_vs_Metro |
0.0
|
-6.458
|
4.57e-07
|
-1.179
|
| HMC_vs_Metro |
0.3
|
-9.258
|
3.68e-10
|
-1.690
|
| HMC_vs_Metro |
0.5
|
-7.081
|
8.65e-08
|
-1.293
|
| HMC_vs_Metro |
0.9
|
-4.518
|
9.65e-05
|
-0.825
|
| HMC_vs_Metro |
0.99
|
-22.291
|
8.51e-20
|
-4.070
|
| HMC_vs_DEMetro_Z |
0.0
|
-16.205
|
4.5e-16
|
-2.959
|
| HMC_vs_DEMetro_Z |
0.3
|
-15.296
|
2.03e-15
|
-2.793
|
| HMC_vs_DEMetro_Z |
0.5
|
-15.915
|
7.23e-16
|
-2.906
|
| HMC_vs_DEMetro_Z |
0.9
|
-13.572
|
4.3e-14
|
-2.478
|
| HMC_vs_DEMetro_Z |
0.99
|
-12.998
|
1.27e-13
|
-2.373
|
| Metro_vs_SMC |
0.0
|
12.516
|
3.24e-13
|
2.285
|
| Metro_vs_SMC |
0.3
|
11.006
|
7.18e-12
|
2.009
|
| Metro_vs_SMC |
0.5
|
7.471
|
3.11e-08
|
1.364
|
| Metro_vs_SMC |
0.9
|
6.873
|
1.5e-07
|
1.255
|
| Metro_vs_SMC |
0.99
|
37.459
|
4.11e-26
|
6.839
|
| DEMetro_Z_vs_SMC |
0.0
|
16.218
|
4.41e-16
|
2.961
|
| DEMetro_Z_vs_SMC |
0.3
|
15.299
|
2.02e-15
|
2.793
|
| DEMetro_Z_vs_SMC |
0.5
|
15.921
|
7.15e-16
|
2.907
|
| DEMetro_Z_vs_SMC |
0.9
|
13.637
|
3.82e-14
|
2.490
|
| DEMetro_Z_vs_SMC |
0.99
|
13.074
|
1.1e-13
|
2.387
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.043 |
0.032 |
0.004 |
3.139 |
| HMC |
0.3 |
0.038 |
0.031 |
0.004 |
1.719 |
| HMC |
0.5 |
0.038 |
0.030 |
0.005 |
1.538 |
| HMC |
0.9 |
0.112 |
0.024 |
0.009 |
9.526 |
| HMC |
0.99 |
0.151 |
0.034 |
0.018 |
6.295 |
| SMC |
0.0 |
0.031 |
0.032 |
0.004 |
-0.110 |
| SMC |
0.3 |
0.033 |
0.031 |
0.004 |
0.403 |
| SMC |
0.5 |
0.032 |
0.030 |
0.005 |
0.323 |
| SMC |
0.9 |
0.027 |
0.024 |
0.009 |
0.329 |
| SMC |
0.99 |
0.025 |
0.034 |
0.018 |
-0.537 |
| Metro |
0.0 |
0.054 |
0.032 |
0.004 |
6.193 |
| Metro |
0.3 |
0.064 |
0.031 |
0.004 |
7.563 |
| Metro |
0.5 |
0.089 |
0.030 |
0.005 |
11.358 |
| Metro |
0.9 |
0.384 |
0.024 |
0.009 |
38.864 |
| Metro |
0.99 |
0.836 |
0.034 |
0.018 |
43.333 |
| DEMetro_Z |
0.0 |
21.853 |
0.032 |
0.004 |
6154.027 |
| DEMetro_Z |
0.3 |
18.609 |
0.031 |
0.004 |
4299.505 |
| DEMetro_Z |
0.5 |
21.187 |
0.030 |
0.005 |
4034.718 |
| DEMetro_Z |
0.9 |
22.521 |
0.024 |
0.009 |
2424.092 |
| DEMetro_Z |
0.99 |
22.987 |
0.034 |
0.018 |
1241.396 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-2.321 |
0.0241 |
-0.533 |
| HMC |
0.3 |
2.716 |
0.00964 |
1.176 |
| HMC |
0.5 |
4.099 |
0.000259 |
3.117 |
| HMC |
0.9 |
7.090 |
6.53e-08 |
8.620 |
| HMC |
0.99 |
5.528 |
5.67e-06 |
14.520 |
| SMC |
0.0 |
-0.890 |
0.377 |
-0.231 |
| SMC |
0.3 |
0.827 |
0.412 |
0.245 |
| SMC |
0.5 |
0.598 |
0.552 |
0.157 |
| SMC |
0.9 |
0.082 |
0.935 |
0.019 |
| SMC |
0.99 |
0.413 |
0.682 |
0.123 |
| Metro |
0.0 |
16.688 |
7.05e-21 |
6.350 |
| Metro |
0.3 |
7.298 |
3.97e-08 |
10.200 |
| Metro |
0.5 |
7.456 |
2.97e-08 |
16.492 |
| Metro |
0.9 |
8.472 |
2.44e-09 |
64.005 |
| Metro |
0.99 |
7.582 |
2.33e-08 |
150.042 |
| DEMetro_Z |
0.0 |
23.129 |
3.09e-20 |
5285.783 |
| DEMetro_Z |
0.3 |
48.657 |
2.34e-29 |
2926.699 |
| DEMetro_Z |
0.5 |
39.077 |
1.23e-26 |
2294.562 |
| DEMetro_Z |
0.9 |
41.280 |
2.58e-27 |
1351.611 |
| DEMetro_Z |
0.99 |
31.765 |
4.38e-24 |
1028.680 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0.0
|
-23.108
|
3.16e-20
|
-4.219
|
| Metro_vs_DEMetro_Z |
0.3
|
-48.483
|
2.6e-29
|
-8.852
|
| Metro_vs_DEMetro_Z |
0.5
|
-39.095
|
1.22e-26
|
-7.138
|
| Metro_vs_DEMetro_Z |
0.9
|
-42.093
|
1.48e-27
|
-7.685
|
| Metro_vs_DEMetro_Z |
0.99
|
-23.869
|
1.29e-20
|
-4.358
|
| DEMetro_Z_vs_SMC |
0.0
|
23.134
|
3.07e-20
|
4.224
|
| DEMetro_Z_vs_SMC |
0.3
|
48.681
|
2.31e-29
|
8.888
|
| DEMetro_Z_vs_SMC |
0.5
|
39.033
|
1.27e-26
|
7.126
|
| DEMetro_Z_vs_SMC |
0.9
|
41.293
|
2.56e-27
|
7.539
|
| DEMetro_Z_vs_SMC |
0.99
|
31.700
|
4.65e-24
|
5.788
|
| HMC_vs_DEMetro_Z |
0.0
|
-23.130
|
3.08e-20
|
-4.223
|
| HMC_vs_DEMetro_Z |
0.3
|
-48.733
|
2.24e-29
|
-8.897
|
| HMC_vs_DEMetro_Z |
0.5
|
-38.918
|
1.39e-26
|
-7.105
|
| HMC_vs_DEMetro_Z |
0.9
|
-41.108
|
2.91e-27
|
-7.505
|
| HMC_vs_DEMetro_Z |
0.99
|
-31.819
|
4.19e-24
|
-5.809
|
| HMC_vs_Metro |
0.0
|
-18.257
|
1.91e-17
|
-3.333
|
| HMC_vs_Metro |
0.3
|
-6.058
|
1.36e-06
|
-1.106
|
| HMC_vs_Metro |
0.5
|
-5.353
|
9.52e-06
|
-0.977
|
| HMC_vs_Metro |
0.9
|
-7.140
|
7.39e-08
|
-1.304
|
| HMC_vs_Metro |
0.99
|
-7.191
|
6.45e-08
|
-1.313
|
| HMC_vs_SMC |
0.0
|
-1.559
|
0.13
|
-0.285
|
| HMC_vs_SMC |
0.3
|
2.231
|
0.0336
|
0.407
|
| HMC_vs_SMC |
0.5
|
3.916
|
0.000502
|
0.715
|
| HMC_vs_SMC |
0.9
|
7.143
|
7.33e-08
|
1.304
|
| HMC_vs_SMC |
0.99
|
5.308
|
1.08e-05
|
0.969
|
| Metro_vs_SMC |
0.0
|
18.154
|
2.22e-17
|
3.315
|
| Metro_vs_SMC |
0.3
|
6.882
|
1.46e-07
|
1.256
|
| Metro_vs_SMC |
0.5
|
7.539
|
2.61e-08
|
1.376
|
| Metro_vs_SMC |
0.9
|
8.489
|
2.36e-09
|
1.550
|
| Metro_vs_SMC |
0.99
|
7.540
|
2.6e-08
|
1.377
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.028 |
0.029 |
0.002 |
-0.533 |
| HMC |
0.3 |
0.033 |
0.029 |
0.003 |
1.176 |
| HMC |
0.5 |
0.041 |
0.027 |
0.004 |
3.117 |
| HMC |
0.9 |
0.088 |
0.024 |
0.007 |
8.620 |
| HMC |
0.99 |
0.141 |
0.024 |
0.008 |
14.520 |
| SMC |
0.0 |
0.029 |
0.029 |
0.002 |
-0.231 |
| SMC |
0.3 |
0.030 |
0.029 |
0.003 |
0.245 |
| SMC |
0.5 |
0.028 |
0.027 |
0.004 |
0.157 |
| SMC |
0.9 |
0.024 |
0.024 |
0.007 |
0.019 |
| SMC |
0.99 |
0.025 |
0.024 |
0.008 |
0.123 |
| Metro |
0.0 |
0.040 |
0.029 |
0.002 |
6.350 |
| Metro |
0.3 |
0.063 |
0.029 |
0.003 |
10.200 |
| Metro |
0.5 |
0.098 |
0.027 |
0.004 |
16.492 |
| Metro |
0.9 |
0.499 |
0.024 |
0.007 |
64.005 |
| Metro |
0.99 |
1.233 |
0.024 |
0.008 |
150.042 |
| DEMetro_Z |
0.0 |
9.084 |
0.029 |
0.002 |
5285.783 |
| DEMetro_Z |
0.3 |
9.760 |
0.029 |
0.003 |
2926.699 |
| DEMetro_Z |
0.5 |
9.926 |
0.027 |
0.004 |
2294.562 |
| DEMetro_Z |
0.9 |
10.055 |
0.024 |
0.007 |
1351.611 |
| DEMetro_Z |
0.99 |
8.307 |
0.024 |
0.008 |
1028.680 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-2.962 |
0.00454 |
-0.676 |
| HMC |
0.3 |
2.593 |
0.0131 |
1.104 |
| HMC |
0.5 |
4.303 |
0.000143 |
3.174 |
| HMC |
0.9 |
7.602 |
1.67e-08 |
9.413 |
| HMC |
0.99 |
5.961 |
1.67e-06 |
12.614 |
| SMC |
0.0 |
-0.513 |
0.61 |
-0.129 |
| SMC |
0.3 |
1.203 |
0.234 |
0.354 |
| SMC |
0.5 |
1.228 |
0.224 |
0.337 |
| SMC |
0.9 |
0.449 |
0.655 |
0.121 |
| SMC |
0.99 |
0.219 |
0.827 |
0.061 |
| Metro |
0.0 |
14.544 |
1.2e-19 |
4.815 |
| Metro |
0.3 |
8.393 |
2e-09 |
9.593 |
| Metro |
0.5 |
8.172 |
4.62e-09 |
16.899 |
| Metro |
0.9 |
9.611 |
1.58e-10 |
59.796 |
| Metro |
0.99 |
13.425 |
5.58e-14 |
121.968 |
| DEMetro_Z |
0.0 |
64.268 |
7.48e-33 |
545.423 |
| DEMetro_Z |
0.3 |
80.072 |
1.14e-35 |
373.254 |
| DEMetro_Z |
0.5 |
55.709 |
4.38e-31 |
339.407 |
| DEMetro_Z |
0.9 |
105.939 |
1.04e-39 |
197.012 |
| DEMetro_Z |
0.99 |
108.870 |
1.6e-40 |
153.380 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0.0
|
64.156
|
8.3e-33
|
11.713
|
| DEMetro_Z_vs_SMC |
0.3
|
79.322
|
1.83e-35
|
14.482
|
| DEMetro_Z_vs_SMC |
0.5
|
55.109
|
6.58e-31
|
10.061
|
| DEMetro_Z_vs_SMC |
0.9
|
104.313
|
6.66e-39
|
19.045
|
| DEMetro_Z_vs_SMC |
0.99
|
106.552
|
3.61e-39
|
19.454
|
| HMC_vs_Metro |
0.0
|
-18.349
|
1.67e-17
|
-3.350
|
| HMC_vs_Metro |
0.3
|
-7.012
|
1.04e-07
|
-1.280
|
| HMC_vs_Metro |
0.5
|
-5.891
|
2.15e-06
|
-1.076
|
| HMC_vs_Metro |
0.9
|
-7.837
|
1.21e-08
|
-1.431
|
| HMC_vs_Metro |
0.99
|
-12.566
|
2.94e-13
|
-2.294
|
| Metro_vs_DEMetro_Z |
0.0
|
-63.625
|
1.05e-32
|
-11.616
|
| Metro_vs_DEMetro_Z |
0.3
|
-77.729
|
3.28e-35
|
-14.191
|
| Metro_vs_DEMetro_Z |
0.5
|
-53.525
|
1.52e-30
|
-9.772
|
| Metro_vs_DEMetro_Z |
0.9
|
-21.429
|
2.51e-19
|
-3.912
|
| Metro_vs_DEMetro_Z |
0.99
|
-3.445
|
0.00176
|
-0.629
|
| HMC_vs_SMC |
0.0
|
-3.101
|
0.00427
|
-0.566
|
| HMC_vs_SMC |
0.3
|
1.908
|
0.0663
|
0.348
|
| HMC_vs_SMC |
0.5
|
3.839
|
0.000619
|
0.701
|
| HMC_vs_SMC |
0.9
|
7.551
|
2.53e-08
|
1.379
|
| HMC_vs_SMC |
0.99
|
5.737
|
3.28e-06
|
1.047
|
| Metro_vs_SMC |
0.0
|
17.410
|
6.79e-17
|
3.179
|
| Metro_vs_SMC |
0.3
|
7.883
|
1.08e-08
|
1.439
|
| Metro_vs_SMC |
0.5
|
8.232
|
4.46e-09
|
1.503
|
| Metro_vs_SMC |
0.9
|
9.667
|
1.41e-10
|
1.765
|
| Metro_vs_SMC |
0.99
|
13.318
|
6.92e-14
|
2.431
|
| HMC_vs_DEMetro_Z |
0.0
|
-64.276
|
7.86e-33
|
-11.735
|
| HMC_vs_DEMetro_Z |
0.3
|
-80.315
|
1.27e-35
|
-14.663
|
| HMC_vs_DEMetro_Z |
0.5
|
-53.745
|
1.35e-30
|
-9.812
|
| HMC_vs_DEMetro_Z |
0.9
|
-90.062
|
4.66e-37
|
-16.443
|
| HMC_vs_DEMetro_Z |
0.99
|
-57.620
|
1.83e-31
|
-10.520
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.013 |
0.014 |
0.002 |
-0.676 |
| HMC |
0.3 |
0.017 |
0.015 |
0.002 |
1.104 |
| HMC |
0.5 |
0.023 |
0.014 |
0.003 |
3.174 |
| HMC |
0.9 |
0.058 |
0.014 |
0.005 |
9.413 |
| HMC |
0.99 |
0.089 |
0.015 |
0.006 |
12.614 |
| SMC |
0.0 |
0.014 |
0.014 |
0.002 |
-0.129 |
| SMC |
0.3 |
0.015 |
0.015 |
0.002 |
0.354 |
| SMC |
0.5 |
0.015 |
0.014 |
0.003 |
0.337 |
| SMC |
0.9 |
0.014 |
0.014 |
0.005 |
0.121 |
| SMC |
0.99 |
0.015 |
0.015 |
0.006 |
0.061 |
| Metro |
0.0 |
0.023 |
0.014 |
0.002 |
4.815 |
| Metro |
0.3 |
0.038 |
0.015 |
0.002 |
9.593 |
| Metro |
0.5 |
0.061 |
0.014 |
0.003 |
16.899 |
| Metro |
0.9 |
0.299 |
0.014 |
0.005 |
59.796 |
| Metro |
0.99 |
0.729 |
0.015 |
0.006 |
121.968 |
| DEMetro_Z |
0.0 |
0.941 |
0.014 |
0.002 |
545.423 |
| DEMetro_Z |
0.3 |
0.940 |
0.015 |
0.002 |
373.254 |
| DEMetro_Z |
0.5 |
0.960 |
0.014 |
0.003 |
339.407 |
| DEMetro_Z |
0.9 |
0.953 |
0.014 |
0.005 |
197.012 |
| DEMetro_Z |
0.99 |
0.914 |
0.015 |
0.006 |
153.380 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
Trace Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Vary_Correlation_with_heavy_Tails
(MvStudentT,
correlation,
30 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-0.460 |
0.647 |
-0.113 |
| HMC |
0.3 |
1.800 |
0.0771 |
0.499 |
| HMC |
0.5 |
-0.014 |
0.989 |
-0.004 |
| HMC |
0.9 |
2.553 |
0.0143 |
1.037 |
| HMC |
0.99 |
2.829 |
0.00744 |
1.416 |
| SMC |
0.0 |
3.443 |
0.00108 |
0.948 |
| SMC |
0.3 |
3.260 |
0.00208 |
1.180 |
| SMC |
0.5 |
2.422 |
0.0192 |
0.827 |
| SMC |
0.9 |
2.978 |
0.00497 |
1.406 |
| SMC |
0.99 |
3.853 |
0.000384 |
1.554 |
| Metro |
0.0 |
3.686 |
0.000567 |
1.250 |
| Metro |
0.3 |
4.251 |
0.000112 |
1.715 |
| Metro |
0.5 |
2.720 |
0.0103 |
1.843 |
| Metro |
0.9 |
4.809 |
3.66e-05 |
4.571 |
| Metro |
0.99 |
3.769 |
0.000746 |
41.472 |
| DEMetro_Z |
0.0 |
4.488 |
4.13e-05 |
1.460 |
| DEMetro_Z |
0.3 |
4.630 |
3.64e-05 |
1.996 |
| DEMetro_Z |
0.5 |
3.035 |
0.00374 |
0.951 |
| DEMetro_Z |
0.9 |
3.112 |
0.00404 |
4.161 |
| DEMetro_Z |
0.99 |
3.856 |
0.00054 |
3.678 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0.0
|
-5.180
|
1.54e-05
|
-0.946
|
| HMC_vs_DEMetro_Z |
0.3
|
-4.161
|
0.000258
|
-0.760
|
| HMC_vs_DEMetro_Z |
0.5
|
-3.067
|
0.00465
|
-0.560
|
| HMC_vs_DEMetro_Z |
0.9
|
-2.362
|
0.0251
|
-0.431
|
| HMC_vs_DEMetro_Z |
0.99
|
-2.552
|
0.0162
|
-0.466
|
| Metro_vs_SMC |
0.0
|
0.805
|
0.427
|
0.147
|
| Metro_vs_SMC |
0.3
|
1.181
|
0.247
|
0.216
|
| Metro_vs_SMC |
0.5
|
1.332
|
0.193
|
0.243
|
| Metro_vs_SMC |
0.9
|
3.035
|
0.00504
|
0.554
|
| Metro_vs_SMC |
0.99
|
3.612
|
0.00113
|
0.659
|
| Metro_vs_DEMetro_Z |
0.0
|
-0.551
|
0.586
|
-0.101
|
| Metro_vs_DEMetro_Z |
0.3
|
-0.494
|
0.625
|
-0.090
|
| Metro_vs_DEMetro_Z |
0.5
|
1.282
|
0.21
|
0.234
|
| Metro_vs_DEMetro_Z |
0.9
|
0.236
|
0.815
|
0.043
|
| Metro_vs_DEMetro_Z |
0.99
|
3.386
|
0.00205
|
0.618
|
| HMC_vs_Metro |
0.0
|
-3.852
|
0.000597
|
-0.703
|
| HMC_vs_Metro |
0.3
|
-2.746
|
0.0103
|
-0.501
|
| HMC_vs_Metro |
0.5
|
-2.728
|
0.0107
|
-0.498
|
| HMC_vs_Metro |
0.9
|
-3.848
|
0.000604
|
-0.702
|
| HMC_vs_Metro |
0.99
|
-3.643
|
0.00104
|
-0.665
|
| HMC_vs_SMC |
0.0
|
-4.363
|
0.000148
|
-0.797
|
| HMC_vs_SMC |
0.3
|
-1.951
|
0.0607
|
-0.356
|
| HMC_vs_SMC |
0.5
|
-2.638
|
0.0133
|
-0.482
|
| HMC_vs_SMC |
0.9
|
-0.651
|
0.52
|
-0.119
|
| HMC_vs_SMC |
0.99
|
-0.212
|
0.833
|
-0.039
|
| DEMetro_Z_vs_SMC |
0.0
|
1.569
|
0.127
|
0.286
|
| DEMetro_Z_vs_SMC |
0.3
|
2.202
|
0.0357
|
0.402
|
| DEMetro_Z_vs_SMC |
0.5
|
0.316
|
0.754
|
0.058
|
| DEMetro_Z_vs_SMC |
0.9
|
2.015
|
0.0532
|
0.368
|
| DEMetro_Z_vs_SMC |
0.99
|
2.303
|
0.0287
|
0.420
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.060 |
0.065 |
0.042 |
-0.113 |
| HMC |
0.3 |
0.076 |
0.056 |
0.040 |
0.499 |
| HMC |
0.5 |
0.068 |
0.068 |
0.046 |
-0.004 |
| HMC |
0.9 |
0.075 |
0.047 |
0.027 |
1.037 |
| HMC |
0.99 |
0.105 |
0.052 |
0.037 |
1.416 |
| SMC |
0.0 |
0.105 |
0.065 |
0.042 |
0.948 |
| SMC |
0.3 |
0.103 |
0.056 |
0.040 |
1.180 |
| SMC |
0.5 |
0.107 |
0.068 |
0.046 |
0.827 |
| SMC |
0.9 |
0.084 |
0.047 |
0.027 |
1.406 |
| SMC |
0.99 |
0.110 |
0.052 |
0.037 |
1.554 |
| Metro |
0.0 |
0.117 |
0.065 |
0.042 |
1.250 |
| Metro |
0.3 |
0.124 |
0.056 |
0.040 |
1.715 |
| Metro |
0.5 |
0.154 |
0.068 |
0.046 |
1.843 |
| Metro |
0.9 |
0.169 |
0.047 |
0.027 |
4.571 |
| Metro |
0.99 |
1.603 |
0.052 |
0.037 |
41.472 |
| DEMetro_Z |
0.0 |
0.126 |
0.065 |
0.042 |
1.460 |
| DEMetro_Z |
0.3 |
0.135 |
0.056 |
0.040 |
1.996 |
| DEMetro_Z |
0.5 |
0.112 |
0.068 |
0.046 |
0.951 |
| DEMetro_Z |
0.9 |
0.158 |
0.047 |
0.027 |
4.161 |
| DEMetro_Z |
0.99 |
0.190 |
0.052 |
0.037 |
3.678 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
0.139 |
0.89 |
0.040 |
| HMC |
0.3 |
-0.122 |
0.903 |
-0.034 |
| HMC |
0.5 |
0.451 |
0.654 |
0.113 |
| HMC |
0.9 |
-0.858 |
0.395 |
-0.189 |
| HMC |
0.99 |
-0.400 |
0.691 |
-0.110 |
| SMC |
0.0 |
2.022 |
0.0489 |
0.431 |
| SMC |
0.3 |
4.721 |
1.59e-05 |
1.334 |
| SMC |
0.5 |
0.970 |
0.336 |
0.225 |
| SMC |
0.9 |
1.767 |
0.0829 |
0.410 |
| SMC |
0.99 |
4.495 |
3.64e-05 |
1.042 |
| Metro |
0.0 |
-1.614 |
0.116 |
-0.308 |
| Metro |
0.3 |
0.540 |
0.591 |
0.169 |
| Metro |
0.5 |
0.658 |
0.513 |
0.169 |
| Metro |
0.9 |
-0.069 |
0.946 |
-0.015 |
| Metro |
0.99 |
1.637 |
0.112 |
6.648 |
| DEMetro_Z |
0.0 |
-0.869 |
0.39 |
-0.177 |
| DEMetro_Z |
0.3 |
0.597 |
0.553 |
0.185 |
| DEMetro_Z |
0.5 |
0.490 |
0.626 |
0.124 |
| DEMetro_Z |
0.9 |
0.996 |
0.328 |
2.698 |
| DEMetro_Z |
0.99 |
-0.037 |
0.97 |
-0.009 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0.0
|
-1.581
|
0.125
|
-0.289
|
| HMC_vs_SMC |
0.3
|
-5.161
|
1.62e-05
|
-0.942
|
| HMC_vs_SMC |
0.5
|
-1.541
|
0.134
|
-0.281
|
| HMC_vs_SMC |
0.9
|
-3.627
|
0.00109
|
-0.662
|
| HMC_vs_SMC |
0.99
|
-4.439
|
0.00012
|
-0.810
|
| Metro_vs_DEMetro_Z |
0.0
|
-1.518
|
0.14
|
-0.277
|
| Metro_vs_DEMetro_Z |
0.3
|
-0.146
|
0.885
|
-0.027
|
| Metro_vs_DEMetro_Z |
0.5
|
0.646
|
0.524
|
0.118
|
| Metro_vs_DEMetro_Z |
0.9
|
-1.002
|
0.325
|
-0.183
|
| Metro_vs_DEMetro_Z |
0.99
|
1.637
|
0.113
|
0.299
|
| HMC_vs_Metro |
0.0
|
1.565
|
0.128
|
0.286
|
| HMC_vs_Metro |
0.3
|
-1.137
|
0.265
|
-0.208
|
| HMC_vs_Metro |
0.5
|
-0.703
|
0.488
|
-0.128
|
| HMC_vs_Metro |
0.9
|
-2.925
|
0.00663
|
-0.534
|
| HMC_vs_Metro |
0.99
|
-1.657
|
0.108
|
-0.302
|
| HMC_vs_DEMetro_Z |
0.0
|
1.116
|
0.274
|
0.204
|
| HMC_vs_DEMetro_Z |
0.3
|
-1.324
|
0.196
|
-0.242
|
| HMC_vs_DEMetro_Z |
0.5
|
-0.300
|
0.766
|
-0.055
|
| HMC_vs_DEMetro_Z |
0.9
|
-1.063
|
0.296
|
-0.194
|
| HMC_vs_DEMetro_Z |
0.99
|
-0.681
|
0.501
|
-0.124
|
| Metro_vs_SMC |
0.0
|
-5.287
|
1.14e-05
|
-0.965
|
| Metro_vs_SMC |
0.3
|
-4.100
|
0.000304
|
-0.749
|
| Metro_vs_SMC |
0.5
|
-0.528
|
0.602
|
-0.096
|
| Metro_vs_SMC |
0.9
|
-2.341
|
0.0263
|
-0.427
|
| Metro_vs_SMC |
0.99
|
1.379
|
0.178
|
0.252
|
| DEMetro_Z_vs_SMC |
0.0
|
-4.039
|
0.00036
|
-0.737
|
| DEMetro_Z_vs_SMC |
0.3
|
-4.187
|
0.00024
|
-0.765
|
| DEMetro_Z_vs_SMC |
0.5
|
-1.449
|
0.158
|
-0.264
|
| DEMetro_Z_vs_SMC |
0.9
|
0.846
|
0.405
|
0.154
|
| DEMetro_Z_vs_SMC |
0.99
|
-4.578
|
8.19e-05
|
-0.836
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
9.675 |
9.112 |
14.240 |
0.040 |
| HMC |
0.3 |
4.529 |
4.697 |
4.977 |
-0.034 |
| HMC |
0.5 |
12.531 |
9.883 |
23.480 |
0.113 |
| HMC |
0.9 |
3.885 |
5.328 |
7.624 |
-0.189 |
| HMC |
0.99 |
5.186 |
6.084 |
8.146 |
-0.110 |
| SMC |
0.0 |
15.246 |
9.112 |
14.240 |
0.431 |
| SMC |
0.3 |
11.335 |
4.697 |
4.977 |
1.334 |
| SMC |
0.5 |
15.168 |
9.883 |
23.480 |
0.225 |
| SMC |
0.9 |
8.457 |
5.328 |
7.624 |
0.410 |
| SMC |
0.99 |
14.572 |
6.084 |
8.146 |
1.042 |
| Metro |
0.0 |
4.724 |
9.112 |
14.240 |
-0.308 |
| Metro |
0.3 |
5.539 |
4.697 |
4.977 |
0.169 |
| Metro |
0.5 |
13.862 |
9.883 |
23.480 |
0.169 |
| Metro |
0.9 |
5.214 |
5.328 |
7.624 |
-0.015 |
| Metro |
0.99 |
60.235 |
6.084 |
8.146 |
6.648 |
| DEMetro_Z |
0.0 |
6.585 |
9.112 |
14.240 |
-0.177 |
| DEMetro_Z |
0.3 |
5.615 |
4.697 |
4.977 |
0.185 |
| DEMetro_Z |
0.5 |
12.789 |
9.883 |
23.480 |
0.124 |
| DEMetro_Z |
0.9 |
25.895 |
5.328 |
7.624 |
2.698 |
| DEMetro_Z |
0.99 |
6.007 |
6.084 |
8.146 |
-0.009 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
2.276 |
0.03 |
2.414 |
| HMC |
0.3 |
3.056 |
0.00395 |
1.339 |
| HMC |
0.5 |
3.555 |
0.00093 |
1.425 |
| HMC |
0.9 |
6.244 |
6.53e-08 |
1.848 |
| HMC |
0.99 |
5.171 |
1.16e-05 |
3.960 |
| SMC |
0.0 |
12.599 |
1.96e-13 |
21.836 |
| SMC |
0.3 |
10.437 |
2.08e-11 |
21.953 |
| SMC |
0.5 |
9.130 |
3.94e-10 |
14.722 |
| SMC |
0.9 |
9.039 |
4.87e-10 |
14.312 |
| SMC |
0.99 |
17.277 |
6e-17 |
37.041 |
| Metro |
0.0 |
7.932 |
4.44e-10 |
3.026 |
| Metro |
0.3 |
7.852 |
1.54e-09 |
3.714 |
| Metro |
0.5 |
4.807 |
3.51e-05 |
4.046 |
| Metro |
0.9 |
8.979 |
1.8e-10 |
5.912 |
| Metro |
0.99 |
4.367 |
0.000146 |
69.076 |
| DEMetro_Z |
0.0 |
5.707 |
2.71e-06 |
5.219 |
| DEMetro_Z |
0.3 |
9.567 |
2.17e-11 |
5.390 |
| DEMetro_Z |
0.5 |
11.244 |
2.89e-15 |
3.771 |
| DEMetro_Z |
0.9 |
2.250 |
0.0321 |
7.228 |
| DEMetro_Z |
0.99 |
5.638 |
3.89e-06 |
8.245 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0.0
|
-2.259
|
0.0316
|
-0.412
|
| Metro_vs_DEMetro_Z |
0.3
|
-2.201
|
0.0358
|
-0.402
|
| Metro_vs_DEMetro_Z |
0.5
|
0.322
|
0.75
|
0.059
|
| Metro_vs_DEMetro_Z |
0.9
|
-0.387
|
0.701
|
-0.071
|
| Metro_vs_DEMetro_Z |
0.99
|
3.759
|
0.000767
|
0.686
|
| DEMetro_Z_vs_SMC |
0.0
|
-8.873
|
9.26e-10
|
-1.620
|
| DEMetro_Z_vs_SMC |
0.3
|
-7.465
|
3.16e-08
|
-1.363
|
| DEMetro_Z_vs_SMC |
0.5
|
-7.182
|
6.62e-08
|
-1.311
|
| DEMetro_Z_vs_SMC |
0.9
|
-1.930
|
0.0635
|
-0.352
|
| DEMetro_Z_vs_SMC |
0.99
|
-10.904
|
8.94e-12
|
-1.991
|
| HMC_vs_DEMetro_Z |
0.0
|
-2.262
|
0.0314
|
-0.413
|
| HMC_vs_DEMetro_Z |
0.3
|
-7.964
|
8.78e-09
|
-1.454
|
| HMC_vs_DEMetro_Z |
0.5
|
-6.488
|
4.21e-07
|
-1.185
|
| HMC_vs_DEMetro_Z |
0.9
|
-1.645
|
0.111
|
-0.300
|
| HMC_vs_DEMetro_Z |
0.99
|
-2.848
|
0.008
|
-0.520
|
| HMC_vs_Metro |
0.0
|
-0.589
|
0.56
|
-0.108
|
| HMC_vs_Metro |
0.3
|
-3.881
|
0.000552
|
-0.709
|
| HMC_vs_Metro |
0.5
|
-2.860
|
0.00777
|
-0.522
|
| HMC_vs_Metro |
0.9
|
-7.097
|
8.27e-08
|
-1.296
|
| HMC_vs_Metro |
0.99
|
-4.118
|
0.00029
|
-0.752
|
| HMC_vs_SMC |
0.0
|
-9.270
|
3.58e-10
|
-1.692
|
| HMC_vs_SMC |
0.3
|
-9.671
|
1.4e-10
|
-1.766
|
| HMC_vs_SMC |
0.5
|
-8.292
|
3.85e-09
|
-1.514
|
| HMC_vs_SMC |
0.9
|
-8.050
|
7.07e-09
|
-1.470
|
| HMC_vs_SMC |
0.99
|
-13.836
|
2.65e-14
|
-2.526
|
| Metro_vs_SMC |
0.0
|
-10.753
|
1.24e-11
|
-1.963
|
| Metro_vs_SMC |
0.3
|
-8.696
|
1.42e-09
|
-1.588
|
| Metro_vs_SMC |
0.5
|
-5.392
|
8.53e-06
|
-0.985
|
| Metro_vs_SMC |
0.9
|
-4.810
|
4.3e-05
|
-0.878
|
| Metro_vs_SMC |
0.99
|
2.031
|
0.0515
|
0.371
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.208 |
0.124 |
0.035 |
2.414 |
| HMC |
0.3 |
0.153 |
0.116 |
0.027 |
1.339 |
| HMC |
0.5 |
0.171 |
0.120 |
0.036 |
1.425 |
| HMC |
0.9 |
0.177 |
0.115 |
0.034 |
1.848 |
| HMC |
0.99 |
0.205 |
0.109 |
0.024 |
3.960 |
| SMC |
0.0 |
0.887 |
0.124 |
0.035 |
21.836 |
| SMC |
0.3 |
0.711 |
0.116 |
0.027 |
21.953 |
| SMC |
0.5 |
0.654 |
0.120 |
0.036 |
14.722 |
| SMC |
0.9 |
0.596 |
0.115 |
0.034 |
14.312 |
| SMC |
0.99 |
1.011 |
0.109 |
0.024 |
37.041 |
| Metro |
0.0 |
0.230 |
0.124 |
0.035 |
3.026 |
| Metro |
0.3 |
0.217 |
0.116 |
0.027 |
3.714 |
| Metro |
0.5 |
0.267 |
0.120 |
0.036 |
4.046 |
| Metro |
0.9 |
0.313 |
0.115 |
0.034 |
5.912 |
| Metro |
0.99 |
1.791 |
0.109 |
0.024 |
69.076 |
| DEMetro_Z |
0.0 |
0.306 |
0.124 |
0.035 |
5.219 |
| DEMetro_Z |
0.3 |
0.262 |
0.116 |
0.027 |
5.390 |
| DEMetro_Z |
0.5 |
0.257 |
0.120 |
0.036 |
3.771 |
| DEMetro_Z |
0.9 |
0.358 |
0.115 |
0.034 |
7.228 |
| DEMetro_Z |
0.99 |
0.310 |
0.109 |
0.024 |
8.245 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
2.044 |
0.0496 |
2.200 |
| HMC |
0.3 |
3.385 |
0.00143 |
1.193 |
| HMC |
0.5 |
2.288 |
0.0289 |
1.901 |
| HMC |
0.9 |
6.524 |
6.45e-08 |
2.650 |
| HMC |
0.99 |
3.990 |
0.000358 |
3.196 |
| SMC |
0.0 |
15.334 |
1.39e-15 |
31.158 |
| SMC |
0.3 |
13.095 |
8.6e-14 |
30.008 |
| SMC |
0.5 |
12.521 |
2.6e-13 |
27.485 |
| SMC |
0.9 |
12.904 |
1.11e-13 |
23.405 |
| SMC |
0.99 |
24.304 |
4.37e-21 |
45.812 |
| Metro |
0.0 |
8.760 |
1.55e-10 |
4.599 |
| Metro |
0.3 |
7.717 |
4.61e-09 |
4.562 |
| Metro |
0.5 |
11.258 |
1.68e-13 |
5.871 |
| Metro |
0.9 |
9.483 |
1.1e-10 |
9.336 |
| Metro |
0.99 |
10.744 |
1.22e-11 |
52.976 |
| DEMetro_Z |
0.0 |
7.587 |
1.27e-08 |
6.476 |
| DEMetro_Z |
0.3 |
10.497 |
5.25e-12 |
7.800 |
| DEMetro_Z |
0.5 |
9.643 |
3.4e-11 |
6.531 |
| DEMetro_Z |
0.9 |
5.826 |
2.11e-06 |
6.439 |
| DEMetro_Z |
0.99 |
8.033 |
5.28e-09 |
9.704 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0.0
|
-12.092
|
7.52e-13
|
-2.208
|
| DEMetro_Z_vs_SMC |
0.3
|
-8.856
|
9.64e-10
|
-1.617
|
| DEMetro_Z_vs_SMC |
0.5
|
-9.928
|
7.77e-11
|
-1.813
|
| DEMetro_Z_vs_SMC |
0.9
|
-7.450
|
3.28e-08
|
-1.360
|
| DEMetro_Z_vs_SMC |
0.99
|
-16.326
|
3.7e-16
|
-2.981
|
| HMC_vs_Metro |
0.0
|
-1.954
|
0.0604
|
-0.357
|
| HMC_vs_Metro |
0.3
|
-5.388
|
8.62e-06
|
-0.984
|
| HMC_vs_Metro |
0.5
|
-4.061
|
0.000339
|
-0.741
|
| HMC_vs_Metro |
0.9
|
-6.514
|
3.93e-07
|
-1.189
|
| HMC_vs_Metro |
0.99
|
-10.052
|
5.86e-11
|
-1.835
|
| Metro_vs_DEMetro_Z |
0.0
|
-2.014
|
0.0534
|
-0.368
|
| Metro_vs_DEMetro_Z |
0.3
|
-3.063
|
0.0047
|
-0.559
|
| Metro_vs_DEMetro_Z |
0.5
|
-0.870
|
0.391
|
-0.159
|
| Metro_vs_DEMetro_Z |
0.9
|
2.040
|
0.0506
|
0.372
|
| Metro_vs_DEMetro_Z |
0.99
|
8.383
|
3.07e-09
|
1.531
|
| HMC_vs_SMC |
0.0
|
-12.145
|
6.77e-13
|
-2.217
|
| HMC_vs_SMC |
0.3
|
-12.184
|
6.26e-13
|
-2.224
|
| HMC_vs_SMC |
0.5
|
-10.615
|
1.68e-11
|
-1.938
|
| HMC_vs_SMC |
0.9
|
-11.281
|
4.01e-12
|
-2.060
|
| HMC_vs_SMC |
0.99
|
-20.389
|
9.74e-19
|
-3.722
|
| Metro_vs_SMC |
0.0
|
-13.299
|
7.17e-14
|
-2.428
|
| Metro_vs_SMC |
0.3
|
-11.277
|
4.04e-12
|
-2.059
|
| Metro_vs_SMC |
0.5
|
-9.810
|
1.02e-10
|
-1.791
|
| Metro_vs_SMC |
0.9
|
-7.031
|
9.87e-08
|
-1.284
|
| Metro_vs_SMC |
0.99
|
1.336
|
0.192
|
0.244
|
| HMC_vs_DEMetro_Z |
0.0
|
-2.980
|
0.00578
|
-0.544
|
| HMC_vs_DEMetro_Z |
0.3
|
-8.140
|
5.63e-09
|
-1.486
|
| HMC_vs_DEMetro_Z |
0.5
|
-3.921
|
0.000495
|
-0.716
|
| HMC_vs_DEMetro_Z |
0.9
|
-2.982
|
0.00575
|
-0.544
|
| HMC_vs_DEMetro_Z |
0.99
|
-4.432
|
0.000122
|
-0.809
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.025 |
0.015 |
0.005 |
2.200 |
| HMC |
0.3 |
0.020 |
0.015 |
0.004 |
1.193 |
| HMC |
0.5 |
0.022 |
0.015 |
0.004 |
1.901 |
| HMC |
0.9 |
0.027 |
0.014 |
0.005 |
2.650 |
| HMC |
0.99 |
0.027 |
0.014 |
0.004 |
3.196 |
| SMC |
0.0 |
0.156 |
0.015 |
0.005 |
31.158 |
| SMC |
0.3 |
0.139 |
0.015 |
0.004 |
30.008 |
| SMC |
0.5 |
0.126 |
0.015 |
0.004 |
27.485 |
| SMC |
0.9 |
0.125 |
0.014 |
0.005 |
23.405 |
| SMC |
0.99 |
0.194 |
0.014 |
0.004 |
45.812 |
| Metro |
0.0 |
0.036 |
0.015 |
0.005 |
4.599 |
| Metro |
0.3 |
0.033 |
0.015 |
0.004 |
4.562 |
| Metro |
0.5 |
0.038 |
0.015 |
0.004 |
5.871 |
| Metro |
0.9 |
0.059 |
0.014 |
0.005 |
9.336 |
| Metro |
0.99 |
0.223 |
0.014 |
0.004 |
52.976 |
| DEMetro_Z |
0.0 |
0.044 |
0.015 |
0.005 |
6.476 |
| DEMetro_Z |
0.3 |
0.047 |
0.015 |
0.004 |
7.800 |
| DEMetro_Z |
0.5 |
0.041 |
0.015 |
0.004 |
6.531 |
| DEMetro_Z |
0.9 |
0.045 |
0.014 |
0.005 |
6.439 |
| DEMetro_Z |
0.99 |
0.052 |
0.014 |
0.004 |
9.704 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-0.181 |
0.857 |
-0.055 |
| HMC |
0.3 |
1.674 |
0.0998 |
0.496 |
| HMC |
0.5 |
1.828 |
0.0728 |
0.466 |
| HMC |
0.9 |
3.374 |
0.00192 |
2.470 |
| HMC |
0.99 |
2.152 |
0.0374 |
0.953 |
| SMC |
0.0 |
2.223 |
0.0306 |
0.715 |
| SMC |
0.3 |
0.968 |
0.337 |
0.231 |
| SMC |
0.5 |
1.612 |
0.113 |
0.453 |
| SMC |
0.9 |
1.448 |
0.155 |
0.573 |
| SMC |
0.99 |
3.517 |
0.00125 |
2.204 |
| Metro |
0.0 |
2.839 |
0.00737 |
1.549 |
| Metro |
0.3 |
1.335 |
0.192 |
4.217 |
| Metro |
0.5 |
1.334 |
0.193 |
4.007 |
| Metro |
0.9 |
5.182 |
1.31e-05 |
5.642 |
| Metro |
0.99 |
4.499 |
0.000101 |
21.123 |
| DEMetro_Z |
0.0 |
4.855 |
1.39e-05 |
1.763 |
| DEMetro_Z |
0.3 |
4.418 |
5.82e-05 |
1.584 |
| DEMetro_Z |
0.5 |
3.346 |
0.00205 |
2.332 |
| DEMetro_Z |
0.9 |
5.239 |
7.6e-06 |
3.035 |
| DEMetro_Z |
0.99 |
4.318 |
0.000132 |
2.924 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0.0
|
-4.145
|
0.000269
|
-0.757
|
| HMC_vs_DEMetro_Z |
0.3
|
-3.361
|
0.00219
|
-0.614
|
| HMC_vs_DEMetro_Z |
0.5
|
-2.642
|
0.0131
|
-0.482
|
| HMC_vs_DEMetro_Z |
0.9
|
-0.662
|
0.513
|
-0.121
|
| HMC_vs_DEMetro_Z |
0.99
|
-2.303
|
0.0286
|
-0.420
|
| Metro_vs_SMC |
0.0
|
2.000
|
0.055
|
0.365
|
| Metro_vs_SMC |
0.3
|
1.270
|
0.214
|
0.232
|
| Metro_vs_SMC |
0.5
|
1.174
|
0.25
|
0.214
|
| Metro_vs_SMC |
0.9
|
4.346
|
0.000155
|
0.793
|
| Metro_vs_SMC |
0.99
|
3.908
|
0.000514
|
0.713
|
| Metro_vs_DEMetro_Z |
0.0
|
-0.361
|
0.721
|
-0.066
|
| Metro_vs_DEMetro_Z |
0.3
|
0.833
|
0.411
|
0.152
|
| Metro_vs_DEMetro_Z |
0.5
|
0.536
|
0.596
|
0.098
|
| Metro_vs_DEMetro_Z |
0.9
|
2.059
|
0.0486
|
0.376
|
| Metro_vs_DEMetro_Z |
0.99
|
3.814
|
0.000662
|
0.696
|
| HMC_vs_Metro |
0.0
|
-2.911
|
0.00686
|
-0.531
|
| HMC_vs_Metro |
0.3
|
-1.219
|
0.233
|
-0.223
|
| HMC_vs_Metro |
0.5
|
-1.182
|
0.247
|
-0.216
|
| HMC_vs_Metro |
0.9
|
-2.245
|
0.0325
|
-0.410
|
| HMC_vs_Metro |
0.99
|
-4.228
|
0.000215
|
-0.772
|
| HMC_vs_SMC |
0.0
|
-2.058
|
0.0487
|
-0.376
|
| HMC_vs_SMC |
0.3
|
1.017
|
0.317
|
0.186
|
| HMC_vs_SMC |
0.5
|
0.052
|
0.959
|
0.010
|
| HMC_vs_SMC |
0.9
|
2.603
|
0.0144
|
0.475
|
| HMC_vs_SMC |
0.99
|
-1.674
|
0.105
|
-0.306
|
| DEMetro_Z_vs_SMC |
0.0
|
2.609
|
0.0142
|
0.476
|
| DEMetro_Z_vs_SMC |
0.3
|
3.711
|
0.000872
|
0.677
|
| DEMetro_Z_vs_SMC |
0.5
|
2.661
|
0.0126
|
0.486
|
| DEMetro_Z_vs_SMC |
0.9
|
3.540
|
0.00137
|
0.646
|
| DEMetro_Z_vs_SMC |
0.99
|
0.742
|
0.464
|
0.135
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.063 |
0.065 |
0.042 |
-0.055 |
| HMC |
0.3 |
0.075 |
0.056 |
0.040 |
0.496 |
| HMC |
0.5 |
0.090 |
0.068 |
0.046 |
0.466 |
| HMC |
0.9 |
0.113 |
0.047 |
0.027 |
2.470 |
| HMC |
0.99 |
0.088 |
0.052 |
0.037 |
0.953 |
| SMC |
0.0 |
0.095 |
0.065 |
0.042 |
0.715 |
| SMC |
0.3 |
0.065 |
0.056 |
0.040 |
0.231 |
| SMC |
0.5 |
0.089 |
0.068 |
0.046 |
0.453 |
| SMC |
0.9 |
0.062 |
0.047 |
0.027 |
0.573 |
| SMC |
0.99 |
0.135 |
0.052 |
0.037 |
2.204 |
| Metro |
0.0 |
0.130 |
0.065 |
0.042 |
1.549 |
| Metro |
0.3 |
0.224 |
0.056 |
0.040 |
4.217 |
| Metro |
0.5 |
0.254 |
0.068 |
0.046 |
4.007 |
| Metro |
0.9 |
0.197 |
0.047 |
0.027 |
5.642 |
| Metro |
0.99 |
0.842 |
0.052 |
0.037 |
21.123 |
| DEMetro_Z |
0.0 |
0.139 |
0.065 |
0.042 |
1.763 |
| DEMetro_Z |
0.3 |
0.119 |
0.056 |
0.040 |
1.584 |
| DEMetro_Z |
0.5 |
0.177 |
0.068 |
0.046 |
2.332 |
| DEMetro_Z |
0.9 |
0.128 |
0.047 |
0.027 |
3.035 |
| DEMetro_Z |
0.99 |
0.162 |
0.052 |
0.037 |
2.924 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
-0.342 |
0.734 |
-0.109 |
| HMC |
0.3 |
1.389 |
0.173 |
0.694 |
| HMC |
0.5 |
0.415 |
0.68 |
0.104 |
| HMC |
0.9 |
0.591 |
0.557 |
0.181 |
| HMC |
0.99 |
-0.292 |
0.771 |
-0.078 |
| SMC |
0.0 |
-0.333 |
0.741 |
-0.064 |
| SMC |
0.3 |
0.617 |
0.54 |
0.176 |
| SMC |
0.5 |
0.407 |
0.686 |
0.101 |
| SMC |
0.9 |
-0.005 |
0.996 |
-0.001 |
| SMC |
0.99 |
1.197 |
0.236 |
0.298 |
| Metro |
0.0 |
-1.499 |
0.142 |
-0.293 |
| Metro |
0.3 |
1.007 |
0.322 |
2.604 |
| Metro |
0.5 |
1.119 |
0.272 |
0.891 |
| Metro |
0.9 |
0.002 |
0.998 |
0.000 |
| Metro |
0.99 |
0.512 |
0.61 |
0.132 |
| DEMetro_Z |
0.0 |
-1.510 |
0.14 |
-0.288 |
| DEMetro_Z |
0.3 |
0.962 |
0.341 |
0.306 |
| DEMetro_Z |
0.5 |
0.635 |
0.528 |
0.161 |
| DEMetro_Z |
0.9 |
-0.204 |
0.839 |
-0.045 |
| DEMetro_Z |
0.99 |
-0.073 |
0.942 |
-0.018 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0.0
|
-0.162
|
0.872
|
-0.030
|
| HMC_vs_SMC |
0.3
|
1.171
|
0.251
|
0.214
|
| HMC_vs_SMC |
0.5
|
0.070
|
0.945
|
0.013
|
| HMC_vs_SMC |
0.9
|
0.745
|
0.462
|
0.136
|
| HMC_vs_SMC |
0.99
|
-1.858
|
0.0734
|
-0.339
|
| Metro_vs_DEMetro_Z |
0.0
|
-0.098
|
0.923
|
-0.018
|
| Metro_vs_DEMetro_Z |
0.3
|
0.906
|
0.372
|
0.165
|
| Metro_vs_DEMetro_Z |
0.5
|
0.976
|
0.337
|
0.178
|
| Metro_vs_DEMetro_Z |
0.9
|
1.099
|
0.281
|
0.201
|
| Metro_vs_DEMetro_Z |
0.99
|
1.130
|
0.268
|
0.206
|
| HMC_vs_Metro |
0.0
|
0.689
|
0.496
|
0.126
|
| HMC_vs_Metro |
0.3
|
-0.868
|
0.392
|
-0.158
|
| HMC_vs_Metro |
0.5
|
-1.039
|
0.307
|
-0.190
|
| HMC_vs_Metro |
0.9
|
0.868
|
0.393
|
0.158
|
| HMC_vs_Metro |
0.99
|
-1.328
|
0.195
|
-0.242
|
| HMC_vs_DEMetro_Z |
0.0
|
0.704
|
0.487
|
0.129
|
| HMC_vs_DEMetro_Z |
0.3
|
0.978
|
0.336
|
0.179
|
| HMC_vs_DEMetro_Z |
0.5
|
-1.214
|
0.235
|
-0.222
|
| HMC_vs_DEMetro_Z |
0.9
|
1.057
|
0.299
|
0.193
|
| HMC_vs_DEMetro_Z |
0.99
|
-0.428
|
0.671
|
-0.078
|
| Metro_vs_SMC |
0.0
|
-2.472
|
0.0195
|
-0.451
|
| Metro_vs_SMC |
0.3
|
0.944
|
0.353
|
0.172
|
| Metro_vs_SMC |
0.5
|
1.056
|
0.3
|
0.193
|
| Metro_vs_SMC |
0.9
|
0.016
|
0.987
|
0.003
|
| Metro_vs_SMC |
0.99
|
-0.905
|
0.373
|
-0.165
|
| DEMetro_Z_vs_SMC |
0.0
|
-2.678
|
0.0121
|
-0.489
|
| DEMetro_Z_vs_SMC |
0.3
|
1.001
|
0.325
|
0.183
|
| DEMetro_Z_vs_SMC |
0.5
|
1.418
|
0.167
|
0.259
|
| DEMetro_Z_vs_SMC |
0.9
|
-0.476
|
0.637
|
-0.087
|
| DEMetro_Z_vs_SMC |
0.99
|
-1.886
|
0.0694
|
-0.344
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
7.564 |
9.112 |
14.240 |
-0.109 |
| HMC |
0.3 |
8.152 |
4.697 |
4.977 |
0.694 |
| HMC |
0.5 |
12.319 |
9.883 |
23.480 |
0.104 |
| HMC |
0.9 |
6.706 |
5.328 |
7.624 |
0.181 |
| HMC |
0.99 |
5.450 |
6.084 |
8.146 |
-0.078 |
| SMC |
0.0 |
8.195 |
9.112 |
14.240 |
-0.064 |
| SMC |
0.3 |
5.571 |
4.697 |
4.977 |
0.176 |
| SMC |
0.5 |
12.253 |
9.883 |
23.480 |
0.101 |
| SMC |
0.9 |
5.320 |
5.328 |
7.624 |
-0.001 |
| SMC |
0.99 |
8.514 |
6.084 |
8.146 |
0.298 |
| Metro |
0.0 |
4.939 |
9.112 |
14.240 |
-0.293 |
| Metro |
0.3 |
17.656 |
4.697 |
4.977 |
2.604 |
| Metro |
0.5 |
30.792 |
9.883 |
23.480 |
0.891 |
| Metro |
0.9 |
5.331 |
5.328 |
7.624 |
0.000 |
| Metro |
0.99 |
7.158 |
6.084 |
8.146 |
0.132 |
| DEMetro_Z |
0.0 |
5.011 |
9.112 |
14.240 |
-0.288 |
| DEMetro_Z |
0.3 |
6.221 |
4.697 |
4.977 |
0.306 |
| DEMetro_Z |
0.5 |
13.653 |
9.883 |
23.480 |
0.161 |
| DEMetro_Z |
0.9 |
4.981 |
5.328 |
7.624 |
-0.045 |
| DEMetro_Z |
0.99 |
5.936 |
6.084 |
8.146 |
-0.018 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
1.831 |
0.0748 |
0.861 |
| HMC |
0.3 |
3.010 |
0.0049 |
1.943 |
| HMC |
0.5 |
3.896 |
0.00028 |
1.233 |
| HMC |
0.9 |
4.292 |
0.000126 |
2.324 |
| HMC |
0.99 |
4.542 |
5.81e-05 |
2.394 |
| SMC |
0.0 |
8.976 |
5.27e-10 |
12.383 |
| SMC |
0.3 |
6.883 |
1.12e-07 |
7.982 |
| SMC |
0.5 |
6.588 |
2.4e-07 |
6.906 |
| SMC |
0.9 |
7.004 |
7.89e-08 |
7.820 |
| SMC |
0.99 |
7.853 |
1.1e-08 |
22.812 |
| Metro |
0.0 |
4.805 |
2.98e-05 |
2.967 |
| Metro |
0.3 |
1.665 |
0.107 |
6.941 |
| Metro |
0.5 |
1.933 |
0.063 |
7.181 |
| Metro |
0.9 |
10.747 |
1.46e-12 |
6.608 |
| Metro |
0.99 |
5.854 |
2.37e-06 |
35.757 |
| DEMetro_Z |
0.0 |
10.716 |
2.23e-14 |
3.711 |
| DEMetro_Z |
0.3 |
11.182 |
4.92e-14 |
4.829 |
| DEMetro_Z |
0.5 |
7.139 |
3.35e-08 |
4.938 |
| DEMetro_Z |
0.9 |
8.839 |
2.77e-11 |
3.490 |
| DEMetro_Z |
0.99 |
5.256 |
1.11e-05 |
6.740 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0.0
|
-1.126
|
0.27
|
-0.206
|
| Metro_vs_DEMetro_Z |
0.3
|
0.506
|
0.617
|
0.092
|
| Metro_vs_DEMetro_Z |
0.5
|
0.581
|
0.566
|
0.106
|
| Metro_vs_DEMetro_Z |
0.9
|
4.272
|
0.00019
|
0.780
|
| Metro_vs_DEMetro_Z |
0.99
|
4.630
|
7.08e-05
|
0.845
|
| DEMetro_Z_vs_SMC |
0.0
|
-6.110
|
1.18e-06
|
-1.115
|
| DEMetro_Z_vs_SMC |
0.3
|
-2.706
|
0.0113
|
-0.494
|
| DEMetro_Z_vs_SMC |
0.5
|
-1.877
|
0.0707
|
-0.343
|
| DEMetro_Z_vs_SMC |
0.9
|
-4.156
|
0.000261
|
-0.759
|
| DEMetro_Z_vs_SMC |
0.99
|
-4.857
|
3.78e-05
|
-0.887
|
| HMC_vs_DEMetro_Z |
0.0
|
-5.383
|
8.75e-06
|
-0.983
|
| HMC_vs_DEMetro_Z |
0.3
|
-4.262
|
0.000195
|
-0.778
|
| HMC_vs_DEMetro_Z |
0.5
|
-5.063
|
2.13e-05
|
-0.924
|
| HMC_vs_DEMetro_Z |
0.9
|
-2.628
|
0.0136
|
-0.480
|
| HMC_vs_DEMetro_Z |
0.99
|
-3.204
|
0.00329
|
-0.585
|
| HMC_vs_Metro |
0.0
|
-2.873
|
0.00753
|
-0.525
|
| HMC_vs_Metro |
0.3
|
-1.303
|
0.203
|
-0.238
|
| HMC_vs_Metro |
0.5
|
-1.592
|
0.122
|
-0.291
|
| HMC_vs_Metro |
0.9
|
-5.098
|
1.93e-05
|
-0.931
|
| HMC_vs_Metro |
0.99
|
-5.410
|
8.13e-06
|
-0.988
|
| HMC_vs_SMC |
0.0
|
-8.175
|
5.15e-09
|
-1.493
|
| HMC_vs_SMC |
0.3
|
-4.543
|
9.01e-05
|
-0.829
|
| HMC_vs_SMC |
0.5
|
-5.256
|
1.24e-05
|
-0.960
|
| HMC_vs_SMC |
0.9
|
-5.176
|
1.56e-05
|
-0.945
|
| HMC_vs_SMC |
0.99
|
-6.934
|
1.27e-07
|
-1.266
|
| Metro_vs_SMC |
0.0
|
-6.406
|
5.26e-07
|
-1.170
|
| Metro_vs_SMC |
0.3
|
-0.247
|
0.806
|
-0.045
|
| Metro_vs_SMC |
0.5
|
0.069
|
0.946
|
0.013
|
| Metro_vs_SMC |
0.9
|
-0.967
|
0.342
|
-0.177
|
| Metro_vs_SMC |
0.99
|
1.804
|
0.0817
|
0.329
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.154 |
0.124 |
0.035 |
0.861 |
| HMC |
0.3 |
0.169 |
0.116 |
0.027 |
1.943 |
| HMC |
0.5 |
0.164 |
0.120 |
0.036 |
1.233 |
| HMC |
0.9 |
0.193 |
0.115 |
0.034 |
2.324 |
| HMC |
0.99 |
0.167 |
0.109 |
0.024 |
2.394 |
| SMC |
0.0 |
0.557 |
0.124 |
0.035 |
12.383 |
| SMC |
0.3 |
0.333 |
0.116 |
0.027 |
7.982 |
| SMC |
0.5 |
0.370 |
0.120 |
0.036 |
6.906 |
| SMC |
0.9 |
0.377 |
0.115 |
0.034 |
7.820 |
| SMC |
0.99 |
0.664 |
0.109 |
0.024 |
22.812 |
| Metro |
0.0 |
0.228 |
0.124 |
0.035 |
2.967 |
| Metro |
0.3 |
0.304 |
0.116 |
0.027 |
6.941 |
| Metro |
0.5 |
0.380 |
0.120 |
0.036 |
7.181 |
| Metro |
0.9 |
0.337 |
0.115 |
0.034 |
6.608 |
| Metro |
0.99 |
0.979 |
0.109 |
0.024 |
35.757 |
| DEMetro_Z |
0.0 |
0.254 |
0.124 |
0.035 |
3.711 |
| DEMetro_Z |
0.3 |
0.247 |
0.116 |
0.027 |
4.829 |
| DEMetro_Z |
0.5 |
0.299 |
0.120 |
0.036 |
4.938 |
| DEMetro_Z |
0.9 |
0.232 |
0.115 |
0.034 |
3.490 |
| DEMetro_Z |
0.99 |
0.273 |
0.109 |
0.024 |
6.740 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
2.007 |
0.0499 |
0.623 |
| HMC |
0.3 |
3.234 |
0.00225 |
1.180 |
| HMC |
0.5 |
2.930 |
0.00502 |
0.927 |
| HMC |
0.9 |
6.390 |
6.2e-08 |
2.222 |
| HMC |
0.99 |
5.771 |
1.38e-06 |
3.151 |
| SMC |
0.0 |
12.604 |
2e-13 |
22.973 |
| SMC |
0.3 |
8.540 |
1.65e-09 |
13.080 |
| SMC |
0.5 |
7.913 |
8.91e-09 |
16.167 |
| SMC |
0.9 |
8.290 |
3.3e-09 |
15.010 |
| SMC |
0.99 |
9.871 |
8.39e-11 |
35.819 |
| Metro |
0.0 |
9.304 |
1.28e-11 |
4.089 |
| Metro |
0.3 |
6.252 |
4.61e-07 |
4.485 |
| Metro |
0.5 |
7.366 |
2.04e-08 |
5.659 |
| Metro |
0.9 |
7.933 |
6.97e-09 |
9.847 |
| Metro |
0.99 |
9.003 |
6.66e-10 |
56.660 |
| DEMetro_Z |
0.0 |
10.299 |
2.38e-12 |
5.509 |
| DEMetro_Z |
0.3 |
10.001 |
8.89e-12 |
6.010 |
| DEMetro_Z |
0.5 |
9.330 |
5.52e-11 |
5.682 |
| DEMetro_Z |
0.9 |
8.241 |
7.77e-10 |
4.459 |
| DEMetro_Z |
0.99 |
6.533 |
2.37e-07 |
5.451 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0.0
|
-9.222
|
4.01e-10
|
-1.684
|
| DEMetro_Z_vs_SMC |
0.3
|
-4.313
|
0.00017
|
-0.787
|
| DEMetro_Z_vs_SMC |
0.5
|
-5.067
|
2.11e-05
|
-0.925
|
| DEMetro_Z_vs_SMC |
0.9
|
-6.114
|
1.17e-06
|
-1.116
|
| DEMetro_Z_vs_SMC |
0.99
|
-7.679
|
1.82e-08
|
-1.402
|
| HMC_vs_Metro |
0.0
|
-8.398
|
2.96e-09
|
-1.533
|
| HMC_vs_Metro |
0.3
|
-4.228
|
0.000215
|
-0.772
|
| HMC_vs_Metro |
0.5
|
-6.477
|
4.34e-07
|
-1.183
|
| HMC_vs_Metro |
0.9
|
-6.118
|
1.15e-06
|
-1.117
|
| HMC_vs_Metro |
0.99
|
-8.345
|
3.38e-09
|
-1.524
|
| Metro_vs_DEMetro_Z |
0.0
|
-2.143
|
0.0406
|
-0.391
|
| Metro_vs_DEMetro_Z |
0.3
|
-1.602
|
0.12
|
-0.293
|
| Metro_vs_DEMetro_Z |
0.5
|
-0.022
|
0.982
|
-0.004
|
| Metro_vs_DEMetro_Z |
0.9
|
3.742
|
0.000802
|
0.683
|
| Metro_vs_DEMetro_Z |
0.99
|
8.030
|
7.43e-09
|
1.466
|
| HMC_vs_SMC |
0.0
|
-13.048
|
1.15e-13
|
-2.382
|
| HMC_vs_SMC |
0.3
|
-7.645
|
1.98e-08
|
-1.396
|
| HMC_vs_SMC |
0.5
|
-7.565
|
2.44e-08
|
-1.381
|
| HMC_vs_SMC |
0.9
|
-7.094
|
8.35e-08
|
-1.295
|
| HMC_vs_SMC |
0.99
|
-8.768
|
1.19e-09
|
-1.601
|
| Metro_vs_SMC |
0.0
|
-10.400
|
2.69e-11
|
-1.899
|
| Metro_vs_SMC |
0.3
|
-5.629
|
4.42e-06
|
-1.028
|
| Metro_vs_SMC |
0.5
|
-4.993
|
2.58e-05
|
-0.912
|
| Metro_vs_SMC |
0.9
|
-2.335
|
0.0267
|
-0.426
|
| Metro_vs_SMC |
0.99
|
2.638
|
0.0133
|
0.482
|
| HMC_vs_DEMetro_Z |
0.0
|
-8.253
|
4.24e-09
|
-1.507
|
| HMC_vs_DEMetro_Z |
0.3
|
-7.004
|
1.06e-07
|
-1.279
|
| HMC_vs_DEMetro_Z |
0.5
|
-7.814
|
1.29e-08
|
-1.427
|
| HMC_vs_DEMetro_Z |
0.9
|
-3.674
|
0.000961
|
-0.671
|
| HMC_vs_DEMetro_Z |
0.99
|
-2.367
|
0.0248
|
-0.432
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.018 |
0.015 |
0.005 |
0.623 |
| HMC |
0.3 |
0.019 |
0.015 |
0.004 |
1.180 |
| HMC |
0.5 |
0.018 |
0.015 |
0.004 |
0.927 |
| HMC |
0.9 |
0.025 |
0.014 |
0.005 |
2.222 |
| HMC |
0.99 |
0.027 |
0.014 |
0.004 |
3.151 |
| SMC |
0.0 |
0.119 |
0.015 |
0.005 |
22.973 |
| SMC |
0.3 |
0.069 |
0.015 |
0.004 |
13.080 |
| SMC |
0.5 |
0.080 |
0.015 |
0.004 |
16.167 |
| SMC |
0.9 |
0.086 |
0.014 |
0.005 |
15.010 |
| SMC |
0.99 |
0.155 |
0.014 |
0.004 |
35.819 |
| Metro |
0.0 |
0.033 |
0.015 |
0.005 |
4.089 |
| Metro |
0.3 |
0.033 |
0.015 |
0.004 |
4.485 |
| Metro |
0.5 |
0.038 |
0.015 |
0.004 |
5.659 |
| Metro |
0.9 |
0.061 |
0.014 |
0.005 |
9.847 |
| Metro |
0.99 |
0.237 |
0.014 |
0.004 |
56.660 |
| DEMetro_Z |
0.0 |
0.040 |
0.015 |
0.005 |
5.509 |
| DEMetro_Z |
0.3 |
0.039 |
0.015 |
0.004 |
6.010 |
| DEMetro_Z |
0.5 |
0.038 |
0.015 |
0.004 |
5.682 |
| DEMetro_Z |
0.9 |
0.035 |
0.014 |
0.005 |
4.459 |
| DEMetro_Z |
0.99 |
0.036 |
0.014 |
0.004 |
5.451 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
KDE + Init Plots
Trace Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Vary_Correlation_with_high_Multimodality
(Mixture,
correlation,
30 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
6.218 |
8.66e-07 |
29.545 |
| HMC |
0.3 |
7.245 |
5.5e-08 |
32.338 |
| HMC |
0.5 |
7.671 |
1.81e-08 |
34.295 |
| HMC |
0.9 |
5.983 |
1.64e-06 |
25.060 |
| HMC |
0.99 |
7.119 |
7.57e-08 |
24.976 |
| SMC |
0.0 |
-0.250 |
0.803 |
-0.062 |
| SMC |
0.3 |
-1.160 |
0.251 |
-0.298 |
| SMC |
0.5 |
0.806 |
0.423 |
0.197 |
| SMC |
0.9 |
-1.132 |
0.263 |
-0.250 |
| SMC |
0.99 |
1.801 |
0.0771 |
0.515 |
| Metro |
0.0 |
7.119 |
7.66e-08 |
32.526 |
| Metro |
0.3 |
6.185 |
9.48e-07 |
29.400 |
| Metro |
0.5 |
7.722 |
1.59e-08 |
35.560 |
| Metro |
0.9 |
4.613 |
7.38e-05 |
20.369 |
| Metro |
0.99 |
6.575 |
3.28e-07 |
27.769 |
| DEMetro_Z |
0.0 |
6.306 |
6.76e-07 |
24.625 |
| DEMetro_Z |
0.3 |
6.026 |
1.46e-06 |
23.430 |
| DEMetro_Z |
0.5 |
7.334 |
4.28e-08 |
24.640 |
| DEMetro_Z |
0.9 |
4.443 |
0.000118 |
20.043 |
| DEMetro_Z |
0.99 |
6.379 |
5.59e-07 |
30.642 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0.0
|
0.845
|
0.405
|
0.154
|
| HMC_vs_DEMetro_Z |
0.3
|
1.385
|
0.176
|
0.253
|
| HMC_vs_DEMetro_Z |
0.5
|
1.511
|
0.142
|
0.276
|
| HMC_vs_DEMetro_Z |
0.9
|
0.803
|
0.429
|
0.147
|
| HMC_vs_DEMetro_Z |
0.99
|
-0.999
|
0.326
|
-0.182
|
| Metro_vs_SMC |
0.0
|
7.110
|
7.99e-08
|
1.298
|
| Metro_vs_SMC |
0.3
|
6.156
|
1.04e-06
|
1.124
|
| Metro_vs_SMC |
0.5
|
7.767
|
1.45e-08
|
1.418
|
| Metro_vs_SMC |
0.9
|
4.655
|
6.6e-05
|
0.850
|
| Metro_vs_SMC |
0.99
|
6.416
|
5.12e-07
|
1.171
|
| Metro_vs_DEMetro_Z |
0.0
|
1.474
|
0.151
|
0.269
|
| Metro_vs_DEMetro_Z |
0.3
|
1.200
|
0.24
|
0.219
|
| Metro_vs_DEMetro_Z |
0.5
|
1.975
|
0.0579
|
0.360
|
| Metro_vs_DEMetro_Z |
0.9
|
0.052
|
0.959
|
0.009
|
| Metro_vs_DEMetro_Z |
0.99
|
-0.468
|
0.643
|
-0.085
|
| HMC_vs_Metro |
0.0
|
-0.759
|
0.454
|
-0.139
|
| HMC_vs_Metro |
0.3
|
0.612
|
0.545
|
0.112
|
| HMC_vs_Metro |
0.5
|
-0.229
|
0.821
|
-0.042
|
| HMC_vs_Metro |
0.9
|
1.148
|
0.26
|
0.210
|
| HMC_vs_Metro |
0.99
|
-0.465
|
0.645
|
-0.085
|
| HMC_vs_SMC |
0.0
|
6.220
|
8.72e-07
|
1.136
|
| HMC_vs_SMC |
0.3
|
7.289
|
5e-08
|
1.331
|
| HMC_vs_SMC |
0.5
|
7.651
|
1.95e-08
|
1.397
|
| HMC_vs_SMC |
0.9
|
5.999
|
1.6e-06
|
1.095
|
| HMC_vs_SMC |
0.99
|
6.930
|
1.29e-07
|
1.265
|
| DEMetro_Z_vs_SMC |
0.0
|
6.352
|
6.09e-07
|
1.160
|
| DEMetro_Z_vs_SMC |
0.3
|
6.048
|
1.4e-06
|
1.104
|
| DEMetro_Z_vs_SMC |
0.5
|
7.265
|
5.32e-08
|
1.326
|
| DEMetro_Z_vs_SMC |
0.9
|
4.548
|
8.9e-05
|
0.830
|
| DEMetro_Z_vs_SMC |
0.99
|
6.218
|
8.78e-07
|
1.135
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
1.697 |
0.080 |
0.055 |
29.545 |
| HMC |
0.3 |
2.175 |
0.089 |
0.065 |
32.338 |
| HMC |
0.5 |
2.384 |
0.091 |
0.067 |
34.295 |
| HMC |
0.9 |
1.939 |
0.089 |
0.074 |
25.060 |
| HMC |
0.99 |
1.646 |
0.075 |
0.063 |
24.976 |
| SMC |
0.0 |
0.077 |
0.080 |
0.055 |
-0.062 |
| SMC |
0.3 |
0.069 |
0.089 |
0.065 |
-0.298 |
| SMC |
0.5 |
0.105 |
0.091 |
0.067 |
0.197 |
| SMC |
0.9 |
0.070 |
0.089 |
0.074 |
-0.250 |
| SMC |
0.99 |
0.107 |
0.075 |
0.063 |
0.515 |
| Metro |
0.0 |
1.860 |
0.080 |
0.055 |
32.526 |
| Metro |
0.3 |
1.985 |
0.089 |
0.065 |
29.400 |
| Metro |
0.5 |
2.469 |
0.091 |
0.067 |
35.560 |
| Metro |
0.9 |
1.593 |
0.089 |
0.074 |
20.369 |
| Metro |
0.99 |
1.822 |
0.075 |
0.063 |
27.769 |
| DEMetro_Z |
0.0 |
1.428 |
0.080 |
0.055 |
24.625 |
| DEMetro_Z |
0.3 |
1.600 |
0.089 |
0.065 |
23.430 |
| DEMetro_Z |
0.5 |
1.739 |
0.091 |
0.067 |
24.640 |
| DEMetro_Z |
0.9 |
1.568 |
0.089 |
0.074 |
20.043 |
| DEMetro_Z |
0.99 |
2.002 |
0.075 |
0.063 |
30.642 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
4.447 |
0.000117 |
56.425 |
| HMC |
0.3 |
5.133 |
1.75e-05 |
87.867 |
| HMC |
0.5 |
5.482 |
6.64e-06 |
83.152 |
| HMC |
0.9 |
4.573 |
8.3e-05 |
74.985 |
| HMC |
0.99 |
5.378 |
8.85e-06 |
41.853 |
| SMC |
0.0 |
-0.265 |
0.792 |
-0.070 |
| SMC |
0.3 |
0.773 |
0.443 |
0.220 |
| SMC |
0.5 |
-0.939 |
0.352 |
-0.206 |
| SMC |
0.9 |
1.773 |
0.0815 |
0.447 |
| SMC |
0.99 |
0.916 |
0.364 |
0.249 |
| Metro |
0.0 |
4.907 |
3.28e-05 |
60.761 |
| Metro |
0.3 |
4.643 |
6.83e-05 |
82.332 |
| Metro |
0.5 |
5.717 |
3.47e-06 |
89.388 |
| Metro |
0.9 |
4.001 |
0.000399 |
67.833 |
| Metro |
0.99 |
5.404 |
8.25e-06 |
66.127 |
| DEMetro_Z |
0.0 |
4.066 |
0.000334 |
38.398 |
| DEMetro_Z |
0.3 |
3.957 |
0.000449 |
54.882 |
| DEMetro_Z |
0.5 |
4.216 |
0.000222 |
44.452 |
| DEMetro_Z |
0.9 |
3.899 |
0.000526 |
66.626 |
| DEMetro_Z |
0.99 |
4.761 |
4.93e-05 |
69.954 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0.0
|
4.453
|
0.000116
|
0.813
|
| HMC_vs_SMC |
0.3
|
5.121
|
1.81e-05
|
0.935
|
| HMC_vs_SMC |
0.5
|
5.501
|
6.32e-06
|
1.004
|
| HMC_vs_SMC |
0.9
|
4.544
|
8.99e-05
|
0.830
|
| HMC_vs_SMC |
0.99
|
5.357
|
9.42e-06
|
0.978
|
| Metro_vs_DEMetro_Z |
0.0
|
1.931
|
0.0633
|
0.353
|
| Metro_vs_DEMetro_Z |
0.3
|
1.505
|
0.143
|
0.275
|
| Metro_vs_DEMetro_Z |
0.5
|
2.419
|
0.0221
|
0.442
|
| Metro_vs_DEMetro_Z |
0.9
|
0.048
|
0.962
|
0.009
|
| Metro_vs_DEMetro_Z |
0.99
|
-0.215
|
0.831
|
-0.039
|
| HMC_vs_Metro |
0.0
|
-0.426
|
0.673
|
-0.078
|
| HMC_vs_Metro |
0.3
|
0.300
|
0.766
|
0.055
|
| HMC_vs_Metro |
0.5
|
-0.318
|
0.753
|
-0.058
|
| HMC_vs_Metro |
0.9
|
0.471
|
0.641
|
0.086
|
| HMC_vs_Metro |
0.99
|
-1.537
|
0.135
|
-0.281
|
| HMC_vs_DEMetro_Z |
0.0
|
1.179
|
0.248
|
0.215
|
| HMC_vs_DEMetro_Z |
0.3
|
1.342
|
0.19
|
0.245
|
| HMC_vs_DEMetro_Z |
0.5
|
1.816
|
0.0798
|
0.331
|
| HMC_vs_DEMetro_Z |
0.9
|
0.349
|
0.73
|
0.064
|
| HMC_vs_DEMetro_Z |
0.99
|
-1.644
|
0.111
|
-0.300
|
| Metro_vs_SMC |
0.0
|
4.908
|
3.28e-05
|
0.896
|
| Metro_vs_SMC |
0.3
|
4.642
|
6.85e-05
|
0.848
|
| Metro_vs_SMC |
0.5
|
5.732
|
3.33e-06
|
1.047
|
| Metro_vs_SMC |
0.9
|
3.973
|
0.00043
|
0.725
|
| Metro_vs_SMC |
0.99
|
5.396
|
8.44e-06
|
0.985
|
| DEMetro_Z_vs_SMC |
0.0
|
4.072
|
0.000329
|
0.743
|
| DEMetro_Z_vs_SMC |
0.3
|
3.954
|
0.000454
|
0.722
|
| DEMetro_Z_vs_SMC |
0.5
|
4.230
|
0.000214
|
0.772
|
| DEMetro_Z_vs_SMC |
0.9
|
3.866
|
0.000574
|
0.706
|
| DEMetro_Z_vs_SMC |
0.99
|
4.750
|
5.09e-05
|
0.867
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
7.044 |
0.169 |
0.122 |
56.425 |
| HMC |
0.3 |
10.033 |
0.159 |
0.112 |
87.867 |
| HMC |
0.5 |
11.699 |
0.179 |
0.139 |
83.152 |
| HMC |
0.9 |
9.313 |
0.163 |
0.122 |
74.985 |
| HMC |
0.99 |
5.790 |
0.181 |
0.134 |
41.853 |
| SMC |
0.0 |
0.161 |
0.169 |
0.122 |
-0.070 |
| SMC |
0.3 |
0.184 |
0.159 |
0.112 |
0.220 |
| SMC |
0.5 |
0.150 |
0.179 |
0.139 |
-0.206 |
| SMC |
0.9 |
0.217 |
0.163 |
0.122 |
0.447 |
| SMC |
0.99 |
0.214 |
0.181 |
0.134 |
0.249 |
| Metro |
0.0 |
7.572 |
0.169 |
0.122 |
60.761 |
| Metro |
0.3 |
9.411 |
0.159 |
0.112 |
82.332 |
| Metro |
0.5 |
12.563 |
0.179 |
0.139 |
89.388 |
| Metro |
0.9 |
8.440 |
0.163 |
0.122 |
67.833 |
| Metro |
0.99 |
9.043 |
0.181 |
0.134 |
66.127 |
| DEMetro_Z |
0.0 |
4.848 |
0.169 |
0.122 |
38.398 |
| DEMetro_Z |
0.3 |
6.326 |
0.159 |
0.112 |
54.882 |
| DEMetro_Z |
0.5 |
6.337 |
0.179 |
0.139 |
44.452 |
| DEMetro_Z |
0.9 |
8.293 |
0.163 |
0.122 |
66.626 |
| DEMetro_Z |
0.99 |
9.556 |
0.181 |
0.134 |
69.954 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
6.106 |
1.18e-06 |
31.933 |
| HMC |
0.3 |
7.086 |
8.39e-08 |
36.402 |
| HMC |
0.5 |
7.614 |
2.11e-08 |
39.150 |
| HMC |
0.9 |
5.832 |
2.49e-06 |
25.986 |
| HMC |
0.99 |
7.238 |
5.54e-08 |
26.072 |
| SMC |
0.0 |
0.140 |
0.889 |
0.035 |
| SMC |
0.3 |
-1.019 |
0.312 |
-0.251 |
| SMC |
0.5 |
0.585 |
0.561 |
0.146 |
| SMC |
0.9 |
-1.105 |
0.274 |
-0.242 |
| SMC |
0.99 |
2.106 |
0.0398 |
0.611 |
| Metro |
0.0 |
7.030 |
9.76e-08 |
37.178 |
| Metro |
0.3 |
6.200 |
9.11e-07 |
32.302 |
| Metro |
0.5 |
7.774 |
1.4e-08 |
40.682 |
| Metro |
0.9 |
4.645 |
6.76e-05 |
20.949 |
| Metro |
0.99 |
6.953 |
1.19e-07 |
29.894 |
| DEMetro_Z |
0.0 |
6.339 |
6.2e-07 |
27.122 |
| DEMetro_Z |
0.3 |
6.031 |
1.44e-06 |
25.401 |
| DEMetro_Z |
0.5 |
7.343 |
4.22e-08 |
27.798 |
| DEMetro_Z |
0.9 |
4.557 |
8.62e-05 |
20.570 |
| DEMetro_Z |
0.99 |
6.478 |
4.28e-07 |
32.526 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0.0
|
1.736
|
0.0932
|
0.317
|
| Metro_vs_DEMetro_Z |
0.3
|
1.319
|
0.198
|
0.241
|
| Metro_vs_DEMetro_Z |
0.5
|
2.083
|
0.0462
|
0.380
|
| Metro_vs_DEMetro_Z |
0.9
|
0.059
|
0.953
|
0.011
|
| Metro_vs_DEMetro_Z |
0.99
|
-0.419
|
0.678
|
-0.077
|
| DEMetro_Z_vs_SMC |
0.0
|
6.361
|
5.94e-07
|
1.161
|
| DEMetro_Z_vs_SMC |
0.3
|
6.053
|
1.38e-06
|
1.105
|
| DEMetro_Z_vs_SMC |
0.5
|
7.284
|
5.06e-08
|
1.330
|
| DEMetro_Z_vs_SMC |
0.9
|
4.647
|
6.76e-05
|
0.848
|
| DEMetro_Z_vs_SMC |
0.99
|
6.300
|
7.02e-07
|
1.150
|
| HMC_vs_DEMetro_Z |
0.0
|
0.768
|
0.449
|
0.140
|
| HMC_vs_DEMetro_Z |
0.3
|
1.528
|
0.137
|
0.279
|
| HMC_vs_DEMetro_Z |
0.5
|
1.577
|
0.126
|
0.288
|
| HMC_vs_DEMetro_Z |
0.9
|
0.846
|
0.404
|
0.155
|
| HMC_vs_DEMetro_Z |
0.99
|
-1.123
|
0.271
|
-0.205
|
| HMC_vs_Metro |
0.0
|
-1.206
|
0.238
|
-0.220
|
| HMC_vs_Metro |
0.3
|
0.727
|
0.473
|
0.133
|
| HMC_vs_Metro |
0.5
|
-0.236
|
0.815
|
-0.043
|
| HMC_vs_Metro |
0.9
|
1.205
|
0.238
|
0.220
|
| HMC_vs_Metro |
0.99
|
-0.621
|
0.54
|
-0.113
|
| HMC_vs_SMC |
0.0
|
6.100
|
1.21e-06
|
1.114
|
| HMC_vs_SMC |
0.3
|
7.123
|
7.73e-08
|
1.300
|
| HMC_vs_SMC |
0.5
|
7.600
|
2.23e-08
|
1.387
|
| HMC_vs_SMC |
0.9
|
5.840
|
2.47e-06
|
1.066
|
| HMC_vs_SMC |
0.99
|
7.026
|
9.98e-08
|
1.283
|
| Metro_vs_SMC |
0.0
|
7.012
|
1.04e-07
|
1.280
|
| Metro_vs_SMC |
0.3
|
6.184
|
9.63e-07
|
1.129
|
| Metro_vs_SMC |
0.5
|
7.824
|
1.25e-08
|
1.428
|
| Metro_vs_SMC |
0.9
|
4.675
|
6.25e-05
|
0.854
|
| Metro_vs_SMC |
0.99
|
6.788
|
1.88e-07
|
1.239
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
1.500 |
0.089 |
0.044 |
31.933 |
| HMC |
0.3 |
2.043 |
0.096 |
0.053 |
36.402 |
| HMC |
0.5 |
2.149 |
0.098 |
0.052 |
39.150 |
| HMC |
0.9 |
1.785 |
0.098 |
0.065 |
25.986 |
| HMC |
0.99 |
1.479 |
0.085 |
0.053 |
26.072 |
| SMC |
0.0 |
0.090 |
0.089 |
0.044 |
0.035 |
| SMC |
0.3 |
0.082 |
0.096 |
0.053 |
-0.251 |
| SMC |
0.5 |
0.105 |
0.098 |
0.052 |
0.146 |
| SMC |
0.9 |
0.082 |
0.098 |
0.065 |
-0.242 |
| SMC |
0.99 |
0.117 |
0.085 |
0.053 |
0.611 |
| Metro |
0.0 |
1.732 |
0.089 |
0.044 |
37.178 |
| Metro |
0.3 |
1.824 |
0.096 |
0.053 |
32.302 |
| Metro |
0.5 |
2.230 |
0.098 |
0.052 |
40.682 |
| Metro |
0.9 |
1.458 |
0.098 |
0.065 |
20.949 |
| Metro |
0.99 |
1.684 |
0.085 |
0.053 |
29.894 |
| DEMetro_Z |
0.0 |
1.287 |
0.089 |
0.044 |
27.122 |
| DEMetro_Z |
0.3 |
1.454 |
0.096 |
0.053 |
25.401 |
| DEMetro_Z |
0.5 |
1.554 |
0.098 |
0.052 |
27.798 |
| DEMetro_Z |
0.9 |
1.434 |
0.098 |
0.065 |
20.570 |
| DEMetro_Z |
0.99 |
1.824 |
0.085 |
0.053 |
32.526 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
6.379 |
5.6e-07 |
33.225 |
| HMC |
0.3 |
7.490 |
2.89e-08 |
32.546 |
| HMC |
0.5 |
7.897 |
1.02e-08 |
36.512 |
| HMC |
0.9 |
6.141 |
1.07e-06 |
29.014 |
| HMC |
0.99 |
7.182 |
6.49e-08 |
31.319 |
| SMC |
0.0 |
-0.265 |
0.792 |
-0.067 |
| SMC |
0.3 |
-0.798 |
0.428 |
-0.193 |
| SMC |
0.5 |
0.679 |
0.5 |
0.167 |
| SMC |
0.9 |
-1.044 |
0.301 |
-0.230 |
| SMC |
0.99 |
2.015 |
0.0488 |
0.591 |
| Metro |
0.0 |
7.290 |
4.91e-08 |
36.624 |
| Metro |
0.3 |
6.398 |
5.3e-07 |
29.385 |
| Metro |
0.5 |
8.019 |
7.48e-09 |
38.137 |
| Metro |
0.9 |
4.835 |
3.99e-05 |
23.835 |
| Metro |
0.99 |
7.071 |
8.73e-08 |
36.130 |
| DEMetro_Z |
0.0 |
6.472 |
4.32e-07 |
28.033 |
| DEMetro_Z |
0.3 |
6.259 |
7.69e-07 |
24.071 |
| DEMetro_Z |
0.5 |
7.634 |
1.97e-08 |
26.933 |
| DEMetro_Z |
0.9 |
4.579 |
8.12e-05 |
23.269 |
| DEMetro_Z |
0.99 |
6.678 |
2.5e-07 |
37.984 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0.0
|
6.522
|
3.84e-07
|
1.191
|
| DEMetro_Z_vs_SMC |
0.3
|
6.269
|
7.64e-07
|
1.144
|
| DEMetro_Z_vs_SMC |
0.5
|
7.563
|
2.45e-08
|
1.381
|
| DEMetro_Z_vs_SMC |
0.9
|
4.662
|
6.48e-05
|
0.851
|
| DEMetro_Z_vs_SMC |
0.99
|
6.533
|
3.73e-07
|
1.193
|
| HMC_vs_Metro |
0.0
|
-0.769
|
0.448
|
-0.140
|
| HMC_vs_Metro |
0.3
|
0.671
|
0.508
|
0.122
|
| HMC_vs_Metro |
0.5
|
-0.286
|
0.777
|
-0.052
|
| HMC_vs_Metro |
0.9
|
1.143
|
0.263
|
0.209
|
| HMC_vs_Metro |
0.99
|
-0.654
|
0.518
|
-0.119
|
| Metro_vs_DEMetro_Z |
0.0
|
1.448
|
0.158
|
0.264
|
| Metro_vs_DEMetro_Z |
0.3
|
1.094
|
0.283
|
0.200
|
| Metro_vs_DEMetro_Z |
0.5
|
1.946
|
0.0613
|
0.355
|
| Metro_vs_DEMetro_Z |
0.9
|
0.080
|
0.937
|
0.015
|
| Metro_vs_DEMetro_Z |
0.99
|
-0.246
|
0.807
|
-0.045
|
| HMC_vs_SMC |
0.0
|
6.392
|
5.46e-07
|
1.167
|
| HMC_vs_SMC |
0.3
|
7.508
|
2.82e-08
|
1.371
|
| HMC_vs_SMC |
0.5
|
7.898
|
1.04e-08
|
1.442
|
| HMC_vs_SMC |
0.9
|
6.140
|
1.09e-06
|
1.121
|
| HMC_vs_SMC |
0.99
|
6.999
|
1.07e-07
|
1.278
|
| Metro_vs_SMC |
0.0
|
7.288
|
5.01e-08
|
1.331
|
| Metro_vs_SMC |
0.3
|
6.364
|
5.89e-07
|
1.162
|
| Metro_vs_SMC |
0.5
|
8.059
|
6.9e-09
|
1.471
|
| Metro_vs_SMC |
0.9
|
4.861
|
3.73e-05
|
0.887
|
| Metro_vs_SMC |
0.99
|
6.922
|
1.32e-07
|
1.264
|
| HMC_vs_DEMetro_Z |
0.0
|
0.812
|
0.423
|
0.148
|
| HMC_vs_DEMetro_Z |
0.3
|
1.342
|
0.19
|
0.245
|
| HMC_vs_DEMetro_Z |
0.5
|
1.439
|
0.161
|
0.263
|
| HMC_vs_DEMetro_Z |
0.9
|
0.811
|
0.424
|
0.148
|
| HMC_vs_DEMetro_Z |
0.99
|
-0.984
|
0.333
|
-0.180
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.236 |
0.011 |
0.007 |
33.225 |
| HMC |
0.3 |
0.303 |
0.012 |
0.009 |
32.546 |
| HMC |
0.5 |
0.330 |
0.012 |
0.009 |
36.512 |
| HMC |
0.9 |
0.270 |
0.012 |
0.009 |
29.014 |
| HMC |
0.99 |
0.235 |
0.010 |
0.007 |
31.319 |
| SMC |
0.0 |
0.011 |
0.011 |
0.007 |
-0.067 |
| SMC |
0.3 |
0.010 |
0.012 |
0.009 |
-0.193 |
| SMC |
0.5 |
0.014 |
0.012 |
0.009 |
0.167 |
| SMC |
0.9 |
0.009 |
0.012 |
0.009 |
-0.230 |
| SMC |
0.99 |
0.014 |
0.010 |
0.007 |
0.591 |
| Metro |
0.0 |
0.259 |
0.011 |
0.007 |
36.624 |
| Metro |
0.3 |
0.274 |
0.012 |
0.009 |
29.385 |
| Metro |
0.5 |
0.345 |
0.012 |
0.009 |
38.137 |
| Metro |
0.9 |
0.224 |
0.012 |
0.009 |
23.835 |
| Metro |
0.99 |
0.269 |
0.010 |
0.007 |
36.130 |
| DEMetro_Z |
0.0 |
0.201 |
0.011 |
0.007 |
28.033 |
| DEMetro_Z |
0.3 |
0.227 |
0.012 |
0.009 |
24.071 |
| DEMetro_Z |
0.5 |
0.247 |
0.012 |
0.009 |
26.933 |
| DEMetro_Z |
0.9 |
0.219 |
0.012 |
0.009 |
23.269 |
| DEMetro_Z |
0.99 |
0.283 |
0.010 |
0.007 |
37.984 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
275.846 |
1.56e-87 |
82.223 |
| HMC |
0.3 |
263.929 |
7.48e-91 |
69.822 |
| HMC |
0.5 |
250.758 |
2.68e-89 |
67.366 |
| HMC |
0.9 |
250.576 |
1.13e-88 |
61.181 |
| HMC |
0.99 |
254.737 |
3.53e-88 |
71.859 |
| SMC |
0.0 |
0.973 |
0.335 |
0.273 |
| SMC |
0.3 |
-0.433 |
0.666 |
-0.114 |
| SMC |
0.5 |
0.267 |
0.791 |
0.064 |
| SMC |
0.9 |
0.140 |
0.89 |
0.034 |
| SMC |
0.99 |
0.538 |
0.592 |
0.134 |
| Metro |
0.0 |
264.816 |
1.94e-84 |
82.116 |
| Metro |
0.3 |
42.949 |
2.36e-28 |
67.712 |
| Metro |
0.5 |
262.219 |
7.36e-91 |
67.529 |
| Metro |
0.9 |
203.290 |
5.09e-80 |
60.959 |
| Metro |
0.99 |
96.507 |
1.08e-41 |
72.241 |
| DEMetro_Z |
0.0 |
8.099 |
6.18e-09 |
55.677 |
| DEMetro_Z |
0.3 |
13.169 |
8.67e-14 |
58.106 |
| DEMetro_Z |
0.5 |
265.204 |
4.31e-91 |
67.582 |
| DEMetro_Z |
0.9 |
235.667 |
3.67e-88 |
61.250 |
| DEMetro_Z |
0.99 |
261.612 |
8.9e-90 |
71.858 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0.0
|
3.802
|
0.000683
|
0.694
|
| HMC_vs_DEMetro_Z |
0.3
|
2.650
|
0.0129
|
0.484
|
| HMC_vs_DEMetro_Z |
0.5
|
-1.062
|
0.297
|
-0.194
|
| HMC_vs_DEMetro_Z |
0.9
|
-0.463
|
0.647
|
-0.085
|
| HMC_vs_DEMetro_Z |
0.99
|
0.004
|
0.997
|
0.001
|
| Metro_vs_SMC |
0.0
|
246.149
|
1.06e-49
|
44.940
|
| Metro_vs_SMC |
0.3
|
41.692
|
1.95e-27
|
7.612
|
| Metro_vs_SMC |
0.5
|
298.268
|
4.04e-52
|
54.456
|
| Metro_vs_SMC |
0.9
|
208.832
|
1.24e-47
|
38.127
|
| Metro_vs_SMC |
0.99
|
89.153
|
6.25e-37
|
16.277
|
| Metro_vs_DEMetro_Z |
0.0
|
3.787
|
0.000712
|
0.691
|
| Metro_vs_DEMetro_Z |
0.3
|
2.191
|
0.0366
|
0.400
|
| Metro_vs_DEMetro_Z |
0.5
|
-0.302
|
0.765
|
-0.055
|
| Metro_vs_DEMetro_Z |
0.9
|
-1.236
|
0.226
|
-0.226
|
| Metro_vs_DEMetro_Z |
0.99
|
0.533
|
0.598
|
0.097
|
| HMC_vs_Metro |
0.0
|
1.260
|
0.218
|
0.230
|
| HMC_vs_Metro |
0.3
|
1.328
|
0.195
|
0.242
|
| HMC_vs_Metro |
0.5
|
-1.257
|
0.219
|
-0.230
|
| HMC_vs_Metro |
0.9
|
1.013
|
0.32
|
0.185
|
| HMC_vs_Metro |
0.99
|
-0.485
|
0.631
|
-0.089
|
| HMC_vs_SMC |
0.0
|
261.355
|
1.86e-50
|
47.717
|
| HMC_vs_SMC |
0.3
|
244.286
|
1.32e-49
|
44.600
|
| HMC_vs_SMC |
0.5
|
293.623
|
6.36e-52
|
53.608
|
| HMC_vs_SMC |
0.9
|
256.870
|
3.07e-50
|
46.898
|
| HMC_vs_SMC |
0.99
|
286.897
|
1.25e-51
|
52.380
|
| DEMetro_Z_vs_SMC |
0.0
|
7.965
|
8.75e-09
|
1.454
|
| DEMetro_Z_vs_SMC |
0.3
|
13.170
|
9.15e-14
|
2.405
|
| DEMetro_Z_vs_SMC |
0.5
|
319.609
|
5.45e-53
|
58.352
|
| DEMetro_Z_vs_SMC |
0.9
|
274.684
|
4.4e-51
|
50.150
|
| DEMetro_Z_vs_SMC |
0.99
|
246.672
|
9.94e-50
|
45.036
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
4.580 |
0.080 |
0.055 |
82.223 |
| HMC |
0.3 |
4.593 |
0.089 |
0.065 |
69.822 |
| HMC |
0.5 |
4.595 |
0.091 |
0.067 |
67.366 |
| HMC |
0.9 |
4.606 |
0.089 |
0.074 |
61.181 |
| HMC |
0.99 |
4.595 |
0.075 |
0.063 |
71.859 |
| SMC |
0.0 |
0.095 |
0.080 |
0.055 |
0.273 |
| SMC |
0.3 |
0.081 |
0.089 |
0.065 |
-0.114 |
| SMC |
0.5 |
0.096 |
0.091 |
0.067 |
0.064 |
| SMC |
0.9 |
0.091 |
0.089 |
0.074 |
0.034 |
| SMC |
0.99 |
0.083 |
0.075 |
0.063 |
0.134 |
| Metro |
0.0 |
4.574 |
0.080 |
0.055 |
82.116 |
| Metro |
0.3 |
4.456 |
0.089 |
0.065 |
67.712 |
| Metro |
0.5 |
4.606 |
0.091 |
0.067 |
67.529 |
| Metro |
0.9 |
4.589 |
0.089 |
0.074 |
60.959 |
| Metro |
0.99 |
4.619 |
0.075 |
0.063 |
72.241 |
| DEMetro_Z |
0.0 |
3.127 |
0.080 |
0.055 |
55.677 |
| DEMetro_Z |
0.3 |
3.837 |
0.089 |
0.065 |
58.106 |
| DEMetro_Z |
0.5 |
4.610 |
0.091 |
0.067 |
67.582 |
| DEMetro_Z |
0.9 |
4.611 |
0.089 |
0.074 |
61.250 |
| DEMetro_Z |
0.99 |
4.595 |
0.075 |
0.063 |
71.858 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
908.425 |
1.49e-121 |
243.815 |
| HMC |
0.3 |
874.472 |
7.84e-114 |
264.448 |
| HMC |
0.5 |
812.539 |
3.67e-119 |
214.267 |
| HMC |
0.9 |
852.375 |
3.05e-117 |
242.860 |
| HMC |
0.99 |
779.715 |
3.18e-115 |
221.554 |
| SMC |
0.0 |
-0.002 |
0.998 |
-0.001 |
| SMC |
0.3 |
0.569 |
0.571 |
0.144 |
| SMC |
0.5 |
-0.034 |
0.973 |
-0.009 |
| SMC |
0.9 |
-0.248 |
0.805 |
-0.059 |
| SMC |
0.99 |
0.387 |
0.701 |
0.099 |
| Metro |
0.0 |
877.976 |
2.32e-119 |
243.793 |
| Metro |
0.3 |
28.935 |
5.88e-23 |
252.140 |
| Metro |
0.5 |
782.484 |
4.14e-117 |
214.340 |
| Metro |
0.9 |
802.938 |
9.21e-112 |
243.041 |
| Metro |
0.99 |
456.962 |
4.04e-73 |
222.229 |
| DEMetro_Z |
0.0 |
7.753 |
1.5e-08 |
163.501 |
| DEMetro_Z |
0.3 |
11.305 |
3.79e-12 |
213.934 |
| DEMetro_Z |
0.5 |
830.904 |
6.67e-120 |
214.163 |
| DEMetro_Z |
0.9 |
838.288 |
9.07e-116 |
243.021 |
| DEMetro_Z |
0.99 |
757.024 |
1.04e-112 |
221.514 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0.0
|
1009.182
|
1.8e-67
|
184.251
|
| HMC_vs_SMC |
0.3
|
1234.659
|
5.21e-70
|
225.417
|
| HMC_vs_SMC |
0.5
|
702.118
|
6.69e-63
|
128.189
|
| HMC_vs_SMC |
0.9
|
872.189
|
1.24e-65
|
159.239
|
| HMC_vs_SMC |
0.99
|
704.252
|
6.13e-63
|
128.578
|
| Metro_vs_DEMetro_Z |
0.0
|
3.811
|
0.000666
|
0.696
|
| Metro_vs_DEMetro_Z |
0.3
|
1.973
|
0.0581
|
0.360
|
| Metro_vs_DEMetro_Z |
0.5
|
2.761
|
0.00989
|
0.504
|
| Metro_vs_DEMetro_Z |
0.9
|
0.150
|
0.882
|
0.027
|
| Metro_vs_DEMetro_Z |
0.99
|
2.007
|
0.0541
|
0.366
|
| HMC_vs_Metro |
0.0
|
0.470
|
0.642
|
0.086
|
| HMC_vs_Metro |
0.3
|
1.418
|
0.167
|
0.259
|
| HMC_vs_Metro |
0.5
|
-1.177
|
0.249
|
-0.215
|
| HMC_vs_Metro |
0.9
|
-1.385
|
0.177
|
-0.253
|
| HMC_vs_Metro |
0.99
|
-1.925
|
0.064
|
-0.352
|
| HMC_vs_DEMetro_Z |
0.0
|
3.811
|
0.000666
|
0.696
|
| HMC_vs_DEMetro_Z |
0.3
|
2.683
|
0.0119
|
0.490
|
| HMC_vs_DEMetro_Z |
0.5
|
1.839
|
0.0762
|
0.336
|
| HMC_vs_DEMetro_Z |
0.9
|
-2.006
|
0.0542
|
-0.366
|
| HMC_vs_DEMetro_Z |
0.99
|
0.480
|
0.635
|
0.088
|
| Metro_vs_SMC |
0.0
|
958.403
|
8.07e-67
|
174.980
|
| Metro_vs_SMC |
0.3
|
28.896
|
6.3e-23
|
5.276
|
| Metro_vs_SMC |
0.5
|
697.736
|
8.02e-63
|
127.389
|
| Metro_vs_SMC |
0.9
|
802.583
|
1.38e-64
|
146.531
|
| Metro_vs_SMC |
0.99
|
431.063
|
9.31e-57
|
78.701
|
| DEMetro_Z_vs_SMC |
0.0
|
7.729
|
1.6e-08
|
1.411
|
| DEMetro_Z_vs_SMC |
0.3
|
11.312
|
3.75e-12
|
2.065
|
| DEMetro_Z_vs_SMC |
0.5
|
737.888
|
1.58e-63
|
134.719
|
| DEMetro_Z_vs_SMC |
0.9
|
834.711
|
4.44e-65
|
152.397
|
| DEMetro_Z_vs_SMC |
0.99
|
721.560
|
3.03e-63
|
131.738
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
29.874 |
0.169 |
0.122 |
243.815 |
| HMC |
0.3 |
29.875 |
0.159 |
0.112 |
264.448 |
| HMC |
0.5 |
29.865 |
0.179 |
0.139 |
214.267 |
| HMC |
0.9 |
29.799 |
0.163 |
0.122 |
242.860 |
| HMC |
0.99 |
29.873 |
0.181 |
0.134 |
221.554 |
| SMC |
0.0 |
0.169 |
0.169 |
0.122 |
-0.001 |
| SMC |
0.3 |
0.175 |
0.159 |
0.112 |
0.144 |
| SMC |
0.5 |
0.177 |
0.179 |
0.139 |
-0.009 |
| SMC |
0.9 |
0.155 |
0.163 |
0.122 |
-0.059 |
| SMC |
0.99 |
0.194 |
0.181 |
0.134 |
0.099 |
| Metro |
0.0 |
29.872 |
0.169 |
0.122 |
243.793 |
| Metro |
0.3 |
28.492 |
0.159 |
0.112 |
252.140 |
| Metro |
0.5 |
29.875 |
0.179 |
0.139 |
214.340 |
| Metro |
0.9 |
29.821 |
0.163 |
0.122 |
243.041 |
| Metro |
0.99 |
29.963 |
0.181 |
0.134 |
222.229 |
| DEMetro_Z |
0.0 |
20.089 |
0.169 |
0.122 |
163.501 |
| DEMetro_Z |
0.3 |
24.199 |
0.159 |
0.112 |
213.934 |
| DEMetro_Z |
0.5 |
29.850 |
0.179 |
0.139 |
214.163 |
| DEMetro_Z |
0.9 |
29.818 |
0.163 |
0.122 |
243.021 |
| DEMetro_Z |
0.99 |
29.867 |
0.181 |
0.134 |
221.514 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
75.274 |
4.69e-36 |
91.543 |
| HMC |
0.3 |
74.113 |
1.99e-36 |
74.755 |
| HMC |
0.5 |
73.658 |
3.31e-36 |
77.223 |
| HMC |
0.9 |
72.751 |
5.75e-37 |
61.484 |
| HMC |
0.99 |
58.198 |
1.46e-32 |
75.134 |
| SMC |
0.0 |
1.192 |
0.238 |
0.345 |
| SMC |
0.3 |
-0.217 |
0.829 |
-0.054 |
| SMC |
0.5 |
0.560 |
0.577 |
0.137 |
| SMC |
0.9 |
-0.093 |
0.926 |
-0.022 |
| SMC |
0.99 |
0.513 |
0.61 |
0.126 |
| Metro |
0.0 |
71.213 |
3.21e-35 |
90.677 |
| Metro |
0.3 |
39.593 |
3.36e-27 |
71.003 |
| Metro |
0.5 |
58.416 |
1.45e-32 |
77.183 |
| Metro |
0.9 |
67.012 |
1.78e-35 |
61.144 |
| Metro |
0.99 |
53.398 |
2.85e-31 |
76.341 |
| DEMetro_Z |
0.0 |
8.148 |
5.47e-09 |
61.714 |
| DEMetro_Z |
0.3 |
12.906 |
1.45e-13 |
63.078 |
| DEMetro_Z |
0.5 |
81.816 |
4.17e-38 |
75.875 |
| DEMetro_Z |
0.9 |
82.010 |
2.77e-39 |
62.347 |
| DEMetro_Z |
0.99 |
63.878 |
5.92e-34 |
76.119 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0.0
|
3.826
|
0.00064
|
0.699
|
| Metro_vs_DEMetro_Z |
0.3
|
1.586
|
0.124
|
0.290
|
| Metro_vs_DEMetro_Z |
0.5
|
0.771
|
0.447
|
0.141
|
| Metro_vs_DEMetro_Z |
0.9
|
-1.151
|
0.259
|
-0.210
|
| Metro_vs_DEMetro_Z |
0.99
|
0.126
|
0.9
|
0.023
|
| DEMetro_Z_vs_SMC |
0.0
|
8.004
|
7.94e-09
|
1.461
|
| DEMetro_Z_vs_SMC |
0.3
|
12.907
|
1.51e-13
|
2.357
|
| DEMetro_Z_vs_SMC |
0.5
|
83.039
|
4.86e-36
|
15.161
|
| DEMetro_Z_vs_SMC |
0.9
|
82.792
|
5.3e-36
|
15.116
|
| DEMetro_Z_vs_SMC |
0.99
|
64.641
|
6.68e-33
|
11.802
|
| HMC_vs_DEMetro_Z |
0.0
|
3.972
|
0.000431
|
0.725
|
| HMC_vs_DEMetro_Z |
0.3
|
2.284
|
0.0299
|
0.417
|
| HMC_vs_DEMetro_Z |
0.5
|
0.982
|
0.334
|
0.179
|
| HMC_vs_DEMetro_Z |
0.9
|
-0.867
|
0.393
|
-0.158
|
| HMC_vs_DEMetro_Z |
0.99
|
-0.602
|
0.552
|
-0.110
|
| HMC_vs_Metro |
0.0
|
0.521
|
0.606
|
0.095
|
| HMC_vs_Metro |
0.3
|
1.785
|
0.0847
|
0.326
|
| HMC_vs_Metro |
0.5
|
0.022
|
0.982
|
0.004
|
| HMC_vs_Metro |
0.9
|
0.269
|
0.79
|
0.049
|
| HMC_vs_Metro |
0.99
|
-0.735
|
0.468
|
-0.134
|
| HMC_vs_SMC |
0.0
|
73.943
|
1.39e-34
|
13.500
|
| HMC_vs_SMC |
0.3
|
75.088
|
8.89e-35
|
13.709
|
| HMC_vs_SMC |
0.5
|
73.512
|
1.64e-34
|
13.421
|
| HMC_vs_SMC |
0.9
|
73.503
|
1.65e-34
|
13.420
|
| HMC_vs_SMC |
0.99
|
58.485
|
1.19e-31
|
10.678
|
| Metro_vs_SMC |
0.0
|
69.259
|
9.15e-34
|
12.645
|
| Metro_vs_SMC |
0.3
|
39.128
|
1.19e-26
|
7.144
|
| Metro_vs_SMC |
0.5
|
56.669
|
2.95e-31
|
10.346
|
| Metro_vs_SMC |
0.9
|
65.415
|
4.74e-33
|
11.943
|
| Metro_vs_SMC |
0.99
|
53.283
|
1.73e-30
|
9.728
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
4.134 |
0.089 |
0.044 |
91.543 |
| HMC |
0.3 |
4.094 |
0.096 |
0.053 |
74.755 |
| HMC |
0.5 |
4.145 |
0.098 |
0.052 |
77.223 |
| HMC |
0.9 |
4.091 |
0.098 |
0.065 |
61.484 |
| HMC |
0.99 |
4.103 |
0.085 |
0.053 |
75.134 |
| SMC |
0.0 |
0.104 |
0.089 |
0.044 |
0.345 |
| SMC |
0.3 |
0.093 |
0.096 |
0.053 |
-0.054 |
| SMC |
0.5 |
0.105 |
0.098 |
0.052 |
0.137 |
| SMC |
0.9 |
0.097 |
0.098 |
0.065 |
-0.022 |
| SMC |
0.99 |
0.092 |
0.085 |
0.053 |
0.126 |
| Metro |
0.0 |
4.096 |
0.089 |
0.044 |
90.677 |
| Metro |
0.3 |
3.893 |
0.096 |
0.053 |
71.003 |
| Metro |
0.5 |
4.143 |
0.098 |
0.052 |
77.183 |
| Metro |
0.9 |
4.068 |
0.098 |
0.065 |
61.144 |
| Metro |
0.99 |
4.168 |
0.085 |
0.053 |
76.341 |
| DEMetro_Z |
0.0 |
2.816 |
0.089 |
0.044 |
61.714 |
| DEMetro_Z |
0.3 |
3.470 |
0.096 |
0.053 |
63.078 |
| DEMetro_Z |
0.5 |
4.074 |
0.098 |
0.052 |
75.875 |
| DEMetro_Z |
0.9 |
4.147 |
0.098 |
0.065 |
62.347 |
| DEMetro_Z |
0.99 |
4.156 |
0.085 |
0.053 |
76.119 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
0.0 |
146.592 |
4.58e-50 |
88.972 |
| HMC |
0.3 |
148.567 |
6.03e-56 |
68.158 |
| HMC |
0.5 |
170.511 |
7.52e-62 |
70.052 |
| HMC |
0.9 |
145.397 |
9.83e-55 |
68.902 |
| HMC |
0.99 |
167.559 |
3.88e-55 |
86.191 |
| SMC |
0.0 |
1.049 |
0.299 |
0.296 |
| SMC |
0.3 |
-0.039 |
0.969 |
-0.010 |
| SMC |
0.5 |
0.604 |
0.548 |
0.144 |
| SMC |
0.9 |
0.232 |
0.817 |
0.059 |
| SMC |
0.99 |
0.682 |
0.498 |
0.180 |
| Metro |
0.0 |
145.287 |
1.09e-49 |
89.690 |
| Metro |
0.3 |
44.793 |
5.75e-29 |
66.269 |
| Metro |
0.5 |
136.549 |
5.83e-52 |
69.820 |
| Metro |
0.9 |
151.264 |
1.9e-56 |
68.913 |
| Metro |
0.99 |
136.023 |
5.04e-48 |
88.494 |
| DEMetro_Z |
0.0 |
8.138 |
5.6e-09 |
60.493 |
| DEMetro_Z |
0.3 |
13.324 |
6.43e-14 |
56.483 |
| DEMetro_Z |
0.5 |
181.411 |
5.76e-66 |
69.107 |
| DEMetro_Z |
0.9 |
154.868 |
2.29e-57 |
69.295 |
| DEMetro_Z |
0.99 |
152.839 |
4.44e-52 |
85.207 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0.0
|
8.012
|
7.77e-09
|
1.463
|
| DEMetro_Z_vs_SMC |
0.3
|
13.329
|
6.78e-14
|
2.434
|
| DEMetro_Z_vs_SMC |
0.5
|
187.405
|
2.86e-46
|
34.215
|
| DEMetro_Z_vs_SMC |
0.9
|
151.843
|
1.27e-43
|
27.723
|
| DEMetro_Z_vs_SMC |
0.99
|
138.194
|
1.94e-42
|
25.231
|
| HMC_vs_Metro |
0.0
|
-0.894
|
0.379
|
-0.163
|
| HMC_vs_Metro |
0.3
|
1.143
|
0.262
|
0.209
|
| HMC_vs_Metro |
0.5
|
0.414
|
0.682
|
0.076
|
| HMC_vs_Metro |
0.9
|
-0.019
|
0.985
|
-0.004
|
| HMC_vs_Metro |
0.99
|
-3.171
|
0.00357
|
-0.579
|
| Metro_vs_DEMetro_Z |
0.0
|
3.919
|
0.000498
|
0.715
|
| Metro_vs_DEMetro_Z |
0.3
|
2.283
|
0.03
|
0.417
|
| Metro_vs_DEMetro_Z |
0.5
|
1.153
|
0.258
|
0.211
|
| Metro_vs_DEMetro_Z |
0.9
|
-0.737
|
0.467
|
-0.135
|
| Metro_vs_DEMetro_Z |
0.99
|
3.562
|
0.0013
|
0.650
|
| HMC_vs_SMC |
0.0
|
154.510
|
7.67e-44
|
28.209
|
| HMC_vs_SMC |
0.3
|
149.219
|
2.1e-43
|
27.243
|
| HMC_vs_SMC |
0.5
|
191.929
|
1.43e-46
|
35.041
|
| HMC_vs_SMC |
0.9
|
146.969
|
3.27e-43
|
26.833
|
| HMC_vs_SMC |
0.99
|
169.879
|
4.92e-45
|
31.015
|
| Metro_vs_SMC |
0.0
|
150.444
|
1.66e-43
|
27.467
|
| Metro_vs_SMC |
0.3
|
43.848
|
4.61e-28
|
8.005
|
| Metro_vs_SMC |
0.5
|
149.020
|
2.19e-43
|
27.207
|
| Metro_vs_SMC |
0.9
|
154.010
|
8.42e-44
|
28.118
|
| Metro_vs_SMC |
0.99
|
144.032
|
5.86e-43
|
26.297
|
| HMC_vs_DEMetro_Z |
0.0
|
3.794
|
0.000697
|
0.693
|
| HMC_vs_DEMetro_Z |
0.3
|
2.769
|
0.00969
|
0.506
|
| HMC_vs_DEMetro_Z |
0.5
|
1.826
|
0.0782
|
0.333
|
| HMC_vs_DEMetro_Z |
0.9
|
-0.730
|
0.471
|
-0.133
|
| HMC_vs_DEMetro_Z |
0.99
|
1.689
|
0.102
|
0.308
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
0.0 |
0.613 |
0.011 |
0.007 |
88.972 |
| HMC |
0.3 |
0.621 |
0.012 |
0.009 |
68.158 |
| HMC |
0.5 |
0.623 |
0.012 |
0.009 |
70.052 |
| HMC |
0.9 |
0.626 |
0.012 |
0.009 |
68.902 |
| HMC |
0.99 |
0.629 |
0.010 |
0.007 |
86.191 |
| SMC |
0.0 |
0.013 |
0.011 |
0.007 |
0.296 |
| SMC |
0.3 |
0.012 |
0.012 |
0.009 |
-0.010 |
| SMC |
0.5 |
0.014 |
0.012 |
0.009 |
0.144 |
| SMC |
0.9 |
0.012 |
0.012 |
0.009 |
0.059 |
| SMC |
0.99 |
0.011 |
0.010 |
0.007 |
0.180 |
| Metro |
0.0 |
0.618 |
0.011 |
0.007 |
89.690 |
| Metro |
0.3 |
0.604 |
0.012 |
0.009 |
66.269 |
| Metro |
0.5 |
0.621 |
0.012 |
0.009 |
69.820 |
| Metro |
0.9 |
0.627 |
0.012 |
0.009 |
68.913 |
| Metro |
0.99 |
0.646 |
0.010 |
0.007 |
88.494 |
| DEMetro_Z |
0.0 |
0.421 |
0.011 |
0.007 |
60.493 |
| DEMetro_Z |
0.3 |
0.516 |
0.012 |
0.009 |
56.483 |
| DEMetro_Z |
0.5 |
0.614 |
0.012 |
0.009 |
69.107 |
| DEMetro_Z |
0.9 |
0.630 |
0.012 |
0.009 |
69.295 |
| DEMetro_Z |
0.99 |
0.622 |
0.010 |
0.007 |
85.207 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
Mode Transitions (scatter)
KDE + Init Plots
Trace Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Vary_Dimension_with_high_correlation
(MvNormal,
dimension,
30 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
0.600 |
0.552 |
0.217 |
| HMC |
5 |
1.637 |
0.108 |
0.586 |
| HMC |
10 |
4.059 |
0.000282 |
2.835 |
| HMC |
15 |
4.955 |
2.29e-05 |
4.181 |
| HMC |
30 |
5.182 |
1.16e-05 |
4.168 |
| SMC |
2 |
-2.265 |
0.0273 |
-0.560 |
| SMC |
5 |
-0.668 |
0.507 |
-0.155 |
| SMC |
10 |
0.020 |
0.984 |
0.006 |
| SMC |
15 |
1.624 |
0.111 |
0.597 |
| SMC |
30 |
0.336 |
0.738 |
0.081 |
| Metro |
2 |
4.688 |
5.47e-05 |
5.628 |
| Metro |
5 |
6.536 |
3.28e-07 |
10.550 |
| Metro |
10 |
7.266 |
5e-08 |
18.734 |
| Metro |
15 |
5.441 |
7.4e-06 |
29.523 |
| Metro |
30 |
8.432 |
2.58e-09 |
27.655 |
| DEMetro_Z |
2 |
3.515 |
0.00105 |
1.418 |
| DEMetro_Z |
5 |
8.058 |
6.92e-09 |
495.082 |
| DEMetro_Z |
10 |
20.055 |
1.52e-18 |
490.731 |
| DEMetro_Z |
15 |
27.851 |
1.76e-22 |
796.734 |
| DEMetro_Z |
30 |
44.001 |
4.11e-28 |
601.670 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-2.745
|
0.0103
|
-0.501
|
| HMC_vs_DEMetro_Z |
1
|
-8.060
|
6.89e-09
|
-1.471
|
| HMC_vs_DEMetro_Z |
2
|
-20.106
|
1.42e-18
|
-3.671
|
| HMC_vs_DEMetro_Z |
3
|
-27.754
|
1.95e-22
|
-5.067
|
| HMC_vs_DEMetro_Z |
4
|
-43.595
|
5.44e-28
|
-7.959
|
| Metro_vs_SMC |
0
|
5.103
|
1.9e-05
|
0.932
|
| Metro_vs_SMC |
1
|
6.800
|
1.82e-07
|
1.242
|
| Metro_vs_SMC |
2
|
7.173
|
6.78e-08
|
1.310
|
| Metro_vs_SMC |
3
|
5.267
|
1.21e-05
|
0.962
|
| Metro_vs_SMC |
4
|
8.482
|
2.4e-09
|
1.549
|
| Metro_vs_DEMetro_Z |
0
|
3.222
|
0.00313
|
0.588
|
| Metro_vs_DEMetro_Z |
1
|
-7.852
|
1.17e-08
|
-1.434
|
| Metro_vs_DEMetro_Z |
2
|
-19.557
|
3.01e-18
|
-3.571
|
| Metro_vs_DEMetro_Z |
3
|
-26.433
|
7.62e-22
|
-4.826
|
| Metro_vs_DEMetro_Z |
4
|
-43.664
|
5.2e-28
|
-7.972
|
| HMC_vs_Metro |
0
|
-4.196
|
0.000235
|
-0.766
|
| HMC_vs_Metro |
1
|
-5.972
|
1.72e-06
|
-1.090
|
| HMC_vs_Metro |
2
|
-6.296
|
7.09e-07
|
-1.149
|
| HMC_vs_Metro |
3
|
-4.594
|
7.83e-05
|
-0.839
|
| HMC_vs_Metro |
4
|
-7.255
|
5.47e-08
|
-1.325
|
| HMC_vs_SMC |
0
|
2.696
|
0.0116
|
0.492
|
| HMC_vs_SMC |
1
|
2.442
|
0.0209
|
0.446
|
| HMC_vs_SMC |
2
|
4.050
|
0.000349
|
0.739
|
| HMC_vs_SMC |
3
|
4.218
|
0.000221
|
0.770
|
| HMC_vs_SMC |
4
|
5.147
|
1.68e-05
|
0.940
|
| DEMetro_Z_vs_SMC |
0
|
5.143
|
1.71e-05
|
0.939
|
| DEMetro_Z_vs_SMC |
1
|
8.055
|
6.97e-09
|
1.471
|
| DEMetro_Z_vs_SMC |
2
|
20.084
|
1.46e-18
|
3.667
|
| DEMetro_Z_vs_SMC |
3
|
27.902
|
1.68e-22
|
5.094
|
| DEMetro_Z_vs_SMC |
4
|
44.004
|
4.17e-28
|
8.034
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.024 |
0.022 |
0.012 |
0.217 |
| HMC |
5 |
0.023 |
0.017 |
0.011 |
0.586 |
| HMC |
10 |
0.053 |
0.020 |
0.012 |
2.835 |
| HMC |
15 |
0.049 |
0.016 |
0.008 |
4.181 |
| HMC |
30 |
0.064 |
0.018 |
0.011 |
4.168 |
| SMC |
2 |
0.015 |
0.022 |
0.012 |
-0.560 |
| SMC |
5 |
0.015 |
0.017 |
0.011 |
-0.155 |
| SMC |
10 |
0.020 |
0.020 |
0.012 |
0.006 |
| SMC |
15 |
0.020 |
0.016 |
0.008 |
0.597 |
| SMC |
30 |
0.019 |
0.018 |
0.011 |
0.081 |
| Metro |
2 |
0.088 |
0.022 |
0.012 |
5.628 |
| Metro |
5 |
0.136 |
0.017 |
0.011 |
10.550 |
| Metro |
10 |
0.238 |
0.020 |
0.012 |
18.734 |
| Metro |
15 |
0.250 |
0.016 |
0.008 |
29.523 |
| Metro |
30 |
0.325 |
0.018 |
0.011 |
27.655 |
| DEMetro_Z |
2 |
0.038 |
0.022 |
0.012 |
1.418 |
| DEMetro_Z |
5 |
5.622 |
0.017 |
0.011 |
495.082 |
| DEMetro_Z |
10 |
5.724 |
0.020 |
0.012 |
490.731 |
| DEMetro_Z |
15 |
6.342 |
0.016 |
0.008 |
796.734 |
| DEMetro_Z |
30 |
6.702 |
0.018 |
0.011 |
601.670 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
3.754 |
0.000655 |
2.461 |
| HMC |
5 |
2.716 |
0.00898 |
0.870 |
| HMC |
10 |
4.364 |
9.92e-05 |
2.289 |
| HMC |
15 |
3.645 |
0.000818 |
1.905 |
| HMC |
30 |
4.719 |
4.66e-05 |
4.302 |
| SMC |
2 |
2.758 |
0.00844 |
1.078 |
| SMC |
5 |
-0.332 |
0.741 |
-0.074 |
| SMC |
10 |
1.082 |
0.284 |
0.333 |
| SMC |
15 |
-0.327 |
0.745 |
-0.089 |
| SMC |
30 |
-0.168 |
0.867 |
-0.044 |
| Metro |
2 |
6.092 |
9.4e-07 |
6.048 |
| Metro |
5 |
7.018 |
6.54e-08 |
6.394 |
| Metro |
10 |
5.958 |
1.72e-06 |
16.191 |
| Metro |
15 |
8.480 |
2.01e-09 |
14.500 |
| Metro |
30 |
5.366 |
9.04e-06 |
19.652 |
| DEMetro_Z |
2 |
4.772 |
2.98e-05 |
2.601 |
| DEMetro_Z |
5 |
5.839 |
2.48e-06 |
5538.286 |
| DEMetro_Z |
10 |
14.127 |
1.56e-14 |
10274.260 |
| DEMetro_Z |
15 |
21.758 |
1.65e-19 |
10114.031 |
| DEMetro_Z |
30 |
38.977 |
1.33e-26 |
12761.003 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
1.734
|
0.0936
|
0.317
|
| HMC_vs_SMC |
1
|
2.924
|
0.00665
|
0.534
|
| HMC_vs_SMC |
2
|
3.031
|
0.00508
|
0.553
|
| HMC_vs_SMC |
3
|
3.691
|
0.000919
|
0.674
|
| HMC_vs_SMC |
4
|
4.806
|
4.34e-05
|
0.878
|
| Metro_vs_DEMetro_Z |
0
|
3.317
|
0.00246
|
0.606
|
| Metro_vs_DEMetro_Z |
1
|
-5.832
|
2.53e-06
|
-1.065
|
| Metro_vs_DEMetro_Z |
2
|
-14.101
|
1.64e-14
|
-2.574
|
| Metro_vs_DEMetro_Z |
3
|
-21.721
|
1.73e-19
|
-3.966
|
| Metro_vs_DEMetro_Z |
4
|
-38.961
|
1.34e-26
|
-7.113
|
| HMC_vs_Metro |
0
|
-3.647
|
0.00103
|
-0.666
|
| HMC_vs_Metro |
1
|
-5.818
|
2.63e-06
|
-1.062
|
| HMC_vs_Metro |
2
|
-5.181
|
1.53e-05
|
-0.946
|
| HMC_vs_Metro |
3
|
-6.960
|
1.19e-07
|
-1.271
|
| HMC_vs_Metro |
4
|
-4.578
|
8.18e-05
|
-0.836
|
| HMC_vs_DEMetro_Z |
0
|
-0.152
|
0.88
|
-0.028
|
| HMC_vs_DEMetro_Z |
1
|
-5.838
|
2.48e-06
|
-1.066
|
| HMC_vs_DEMetro_Z |
2
|
-14.123
|
1.57e-14
|
-2.579
|
| HMC_vs_DEMetro_Z |
3
|
-21.762
|
1.65e-19
|
-3.973
|
| HMC_vs_DEMetro_Z |
4
|
-38.986
|
1.32e-26
|
-7.118
|
| Metro_vs_SMC |
0
|
4.992
|
2.59e-05
|
0.911
|
| Metro_vs_SMC |
1
|
7.271
|
5.23e-08
|
1.328
|
| Metro_vs_SMC |
2
|
5.841
|
2.46e-06
|
1.066
|
| Metro_vs_SMC |
3
|
8.450
|
2.6e-09
|
1.543
|
| Metro_vs_SMC |
4
|
5.387
|
8.66e-06
|
0.984
|
| DEMetro_Z_vs_SMC |
0
|
2.798
|
0.00905
|
0.511
|
| DEMetro_Z_vs_SMC |
1
|
5.839
|
2.48e-06
|
1.066
|
| DEMetro_Z_vs_SMC |
2
|
14.127
|
1.56e-14
|
2.579
|
| DEMetro_Z_vs_SMC |
3
|
21.759
|
1.65e-19
|
3.973
|
| DEMetro_Z_vs_SMC |
4
|
38.979
|
1.33e-26
|
7.117
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.047 |
0.020 |
0.011 |
2.461 |
| HMC |
5 |
0.050 |
0.031 |
0.022 |
0.870 |
| HMC |
10 |
0.056 |
0.026 |
0.013 |
2.289 |
| HMC |
15 |
0.061 |
0.031 |
0.016 |
1.905 |
| HMC |
30 |
0.090 |
0.029 |
0.014 |
4.302 |
| SMC |
2 |
0.032 |
0.020 |
0.011 |
1.078 |
| SMC |
5 |
0.029 |
0.031 |
0.022 |
-0.074 |
| SMC |
10 |
0.031 |
0.026 |
0.013 |
0.333 |
| SMC |
15 |
0.029 |
0.031 |
0.016 |
-0.089 |
| SMC |
30 |
0.029 |
0.029 |
0.014 |
-0.044 |
| Metro |
2 |
0.087 |
0.020 |
0.011 |
6.048 |
| Metro |
5 |
0.173 |
0.031 |
0.022 |
6.394 |
| Metro |
10 |
0.232 |
0.026 |
0.013 |
16.191 |
| Metro |
15 |
0.261 |
0.031 |
0.016 |
14.500 |
| Metro |
30 |
0.307 |
0.029 |
0.014 |
19.652 |
| DEMetro_Z |
2 |
0.049 |
0.020 |
0.011 |
2.601 |
| DEMetro_Z |
5 |
123.310 |
0.031 |
0.022 |
5538.286 |
| DEMetro_Z |
10 |
130.393 |
0.026 |
0.013 |
10274.260 |
| DEMetro_Z |
15 |
160.845 |
0.031 |
0.016 |
10114.031 |
| DEMetro_Z |
30 |
180.332 |
0.029 |
0.014 |
12761.003 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
2.462 |
0.018 |
1.022 |
| HMC |
5 |
3.500 |
0.00112 |
1.456 |
| HMC |
10 |
5.416 |
5.74e-06 |
4.246 |
| HMC |
15 |
6.766 |
1.49e-07 |
7.308 |
| HMC |
30 |
7.100 |
5.37e-08 |
6.693 |
| SMC |
2 |
-1.612 |
0.112 |
-0.423 |
| SMC |
5 |
-0.640 |
0.525 |
-0.143 |
| SMC |
10 |
0.564 |
0.575 |
0.150 |
| SMC |
15 |
1.807 |
0.0777 |
0.721 |
| SMC |
30 |
0.166 |
0.869 |
0.038 |
| Metro |
2 |
6.004 |
1.37e-06 |
8.157 |
| Metro |
5 |
9.942 |
5.74e-11 |
16.092 |
| Metro |
10 |
9.749 |
1.09e-10 |
29.661 |
| Metro |
15 |
6.971 |
1.15e-07 |
50.079 |
| Metro |
30 |
11.431 |
2.73e-12 |
41.283 |
| DEMetro_Z |
2 |
5.793 |
9.73e-07 |
2.677 |
| DEMetro_Z |
5 |
13.240 |
8.02e-14 |
1098.317 |
| DEMetro_Z |
10 |
28.428 |
9.95e-23 |
1292.195 |
| DEMetro_Z |
15 |
44.986 |
2.22e-28 |
2401.913 |
| DEMetro_Z |
30 |
85.928 |
1.79e-36 |
1581.502 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
3.777
|
0.000731
|
0.690
|
| Metro_vs_DEMetro_Z |
1
|
-12.995
|
1.28e-13
|
-2.372
|
| Metro_vs_DEMetro_Z |
2
|
-28.048
|
1.45e-22
|
-5.121
|
| Metro_vs_DEMetro_Z |
3
|
-44.511
|
3e-28
|
-8.127
|
| Metro_vs_DEMetro_Z |
4
|
-87.683
|
1.01e-36
|
-16.009
|
| DEMetro_Z_vs_SMC |
0
|
7.161
|
7e-08
|
1.307
|
| DEMetro_Z_vs_SMC |
1
|
13.239
|
8.03e-14
|
2.417
|
| DEMetro_Z_vs_SMC |
2
|
28.404
|
1.02e-22
|
5.186
|
| DEMetro_Z_vs_SMC |
3
|
45.022
|
2.17e-28
|
8.220
|
| DEMetro_Z_vs_SMC |
4
|
85.902
|
1.83e-36
|
15.684
|
| HMC_vs_DEMetro_Z |
0
|
-2.830
|
0.00837
|
-0.517
|
| HMC_vs_DEMetro_Z |
1
|
-13.235
|
8.09e-14
|
-2.416
|
| HMC_vs_DEMetro_Z |
2
|
-28.510
|
9.19e-23
|
-5.205
|
| HMC_vs_DEMetro_Z |
3
|
-44.970
|
2.24e-28
|
-8.210
|
| HMC_vs_DEMetro_Z |
4
|
-84.918
|
2.55e-36
|
-15.504
|
| HMC_vs_Metro |
0
|
-4.800
|
4.43e-05
|
-0.876
|
| HMC_vs_Metro |
1
|
-8.443
|
2.64e-09
|
-1.542
|
| HMC_vs_Metro |
2
|
-8.863
|
9.48e-10
|
-1.618
|
| HMC_vs_Metro |
3
|
-5.950
|
1.83e-06
|
-1.086
|
| HMC_vs_Metro |
4
|
-10.144
|
4.77e-11
|
-1.852
|
| HMC_vs_SMC |
0
|
4.228
|
0.000215
|
0.772
|
| HMC_vs_SMC |
1
|
4.132
|
0.000279
|
0.754
|
| HMC_vs_SMC |
2
|
5.286
|
1.15e-05
|
0.965
|
| HMC_vs_SMC |
3
|
6.057
|
1.36e-06
|
1.106
|
| HMC_vs_SMC |
4
|
6.915
|
1.34e-07
|
1.263
|
| Metro_vs_SMC |
0
|
6.198
|
9.27e-07
|
1.132
|
| Metro_vs_SMC |
1
|
10.301
|
3.36e-11
|
1.881
|
| Metro_vs_SMC |
2
|
9.612
|
1.61e-10
|
1.755
|
| Metro_vs_SMC |
3
|
6.805
|
1.8e-07
|
1.242
|
| Metro_vs_SMC |
4
|
11.403
|
3.1e-12
|
2.082
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.036 |
0.028 |
0.008 |
1.022 |
| HMC |
5 |
0.035 |
0.024 |
0.007 |
1.456 |
| HMC |
10 |
0.054 |
0.025 |
0.007 |
4.246 |
| HMC |
15 |
0.053 |
0.023 |
0.004 |
7.308 |
| HMC |
30 |
0.070 |
0.025 |
0.007 |
6.693 |
| SMC |
2 |
0.025 |
0.028 |
0.008 |
-0.423 |
| SMC |
5 |
0.023 |
0.024 |
0.007 |
-0.143 |
| SMC |
10 |
0.026 |
0.025 |
0.007 |
0.150 |
| SMC |
15 |
0.026 |
0.023 |
0.004 |
0.721 |
| SMC |
30 |
0.025 |
0.025 |
0.007 |
0.038 |
| Metro |
2 |
0.091 |
0.028 |
0.008 |
8.157 |
| Metro |
5 |
0.143 |
0.024 |
0.007 |
16.092 |
| Metro |
10 |
0.227 |
0.025 |
0.007 |
29.661 |
| Metro |
15 |
0.230 |
0.023 |
0.004 |
50.079 |
| Metro |
30 |
0.302 |
0.025 |
0.007 |
41.283 |
| DEMetro_Z |
2 |
0.049 |
0.028 |
0.008 |
2.677 |
| DEMetro_Z |
5 |
8.170 |
0.024 |
0.007 |
1098.317 |
| DEMetro_Z |
10 |
8.837 |
0.025 |
0.007 |
1292.195 |
| DEMetro_Z |
15 |
9.964 |
0.023 |
0.004 |
2401.913 |
| DEMetro_Z |
30 |
10.643 |
0.025 |
0.007 |
1581.502 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
1.944 |
0.0585 |
0.795 |
| HMC |
5 |
3.270 |
0.00191 |
1.040 |
| HMC |
10 |
6.009 |
9.39e-07 |
4.308 |
| HMC |
15 |
6.560 |
2.12e-07 |
5.271 |
| HMC |
30 |
7.261 |
2.69e-08 |
5.489 |
| SMC |
2 |
-1.574 |
0.121 |
-0.412 |
| SMC |
5 |
-1.080 |
0.285 |
-0.242 |
| SMC |
10 |
1.312 |
0.195 |
0.384 |
| SMC |
15 |
0.969 |
0.337 |
0.339 |
| SMC |
30 |
-0.460 |
0.647 |
-0.101 |
| Metro |
2 |
5.802 |
2.37e-06 |
7.393 |
| Metro |
5 |
11.968 |
3.73e-13 |
11.965 |
| Metro |
10 |
12.553 |
2.41e-13 |
26.745 |
| Metro |
15 |
8.360 |
3.18e-09 |
40.117 |
| Metro |
30 |
11.436 |
2.55e-12 |
30.635 |
| DEMetro_Z |
2 |
4.490 |
5.62e-05 |
1.925 |
| DEMetro_Z |
5 |
42.304 |
8.25e-28 |
111.762 |
| DEMetro_Z |
10 |
61.896 |
1.1e-32 |
139.765 |
| DEMetro_Z |
15 |
59.948 |
3.78e-32 |
175.702 |
| DEMetro_Z |
30 |
118.412 |
4.76e-44 |
94.855 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
6.175
|
9.86e-07
|
1.127
|
| DEMetro_Z_vs_SMC |
1
|
42.301
|
1.29e-27
|
7.723
|
| DEMetro_Z_vs_SMC |
2
|
61.138
|
3.32e-32
|
11.162
|
| DEMetro_Z_vs_SMC |
3
|
59.097
|
8.83e-32
|
10.790
|
| DEMetro_Z_vs_SMC |
4
|
122.191
|
6.85e-41
|
22.309
|
| HMC_vs_Metro |
0
|
-4.824
|
4.14e-05
|
-0.881
|
| HMC_vs_Metro |
1
|
-10.483
|
2.24e-11
|
-1.914
|
| HMC_vs_Metro |
2
|
-10.505
|
2.13e-11
|
-1.918
|
| HMC_vs_Metro |
3
|
-7.129
|
7.62e-08
|
-1.301
|
| HMC_vs_Metro |
4
|
-9.919
|
7.93e-11
|
-1.811
|
| Metro_vs_DEMetro_Z |
0
|
4.216
|
0.000222
|
0.770
|
| Metro_vs_DEMetro_Z |
1
|
-35.381
|
2.08e-25
|
-6.460
|
| Metro_vs_DEMetro_Z |
2
|
-39.687
|
7.94e-27
|
-7.246
|
| Metro_vs_DEMetro_Z |
3
|
-23.832
|
1.35e-20
|
-4.351
|
| Metro_vs_DEMetro_Z |
4
|
-24.521
|
6.14e-21
|
-4.477
|
| HMC_vs_SMC |
0
|
2.960
|
0.00607
|
0.540
|
| HMC_vs_SMC |
1
|
4.322
|
0.000166
|
0.789
|
| HMC_vs_SMC |
2
|
5.404
|
8.26e-06
|
0.987
|
| HMC_vs_SMC |
3
|
6.080
|
1.28e-06
|
1.110
|
| HMC_vs_SMC |
4
|
7.148
|
7.24e-08
|
1.305
|
| Metro_vs_SMC |
0
|
6.117
|
1.16e-06
|
1.117
|
| Metro_vs_SMC |
1
|
12.543
|
3.07e-13
|
2.290
|
| Metro_vs_SMC |
2
|
12.224
|
5.77e-13
|
2.232
|
| Metro_vs_SMC |
3
|
8.191
|
4.96e-09
|
1.495
|
| Metro_vs_SMC |
4
|
11.430
|
2.92e-12
|
2.087
|
| HMC_vs_DEMetro_Z |
0
|
-1.973
|
0.0581
|
-0.360
|
| HMC_vs_DEMetro_Z |
1
|
-42.578
|
1.07e-27
|
-7.774
|
| HMC_vs_DEMetro_Z |
2
|
-55.435
|
5.56e-31
|
-10.121
|
| HMC_vs_DEMetro_Z |
3
|
-55.813
|
4.57e-31
|
-10.190
|
| HMC_vs_DEMetro_Z |
4
|
-86.901
|
1.31e-36
|
-15.866
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.018 |
0.014 |
0.005 |
0.795 |
| HMC |
5 |
0.020 |
0.014 |
0.006 |
1.040 |
| HMC |
10 |
0.032 |
0.014 |
0.004 |
4.308 |
| HMC |
15 |
0.032 |
0.014 |
0.003 |
5.271 |
| HMC |
30 |
0.047 |
0.015 |
0.006 |
5.489 |
| SMC |
2 |
0.012 |
0.014 |
0.005 |
-0.412 |
| SMC |
5 |
0.012 |
0.014 |
0.006 |
-0.242 |
| SMC |
10 |
0.015 |
0.014 |
0.004 |
0.384 |
| SMC |
15 |
0.015 |
0.014 |
0.003 |
0.339 |
| SMC |
30 |
0.014 |
0.015 |
0.006 |
-0.101 |
| Metro |
2 |
0.049 |
0.014 |
0.005 |
7.393 |
| Metro |
5 |
0.089 |
0.014 |
0.006 |
11.965 |
| Metro |
10 |
0.131 |
0.014 |
0.004 |
26.745 |
| Metro |
15 |
0.150 |
0.014 |
0.003 |
40.117 |
| Metro |
30 |
0.193 |
0.015 |
0.006 |
30.635 |
| DEMetro_Z |
2 |
0.023 |
0.014 |
0.005 |
1.925 |
| DEMetro_Z |
5 |
0.712 |
0.014 |
0.006 |
111.762 |
| DEMetro_Z |
10 |
0.625 |
0.014 |
0.004 |
139.765 |
| DEMetro_Z |
15 |
0.609 |
0.014 |
0.003 |
175.702 |
| DEMetro_Z |
30 |
0.566 |
0.015 |
0.006 |
94.855 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
1.719 |
0.093 |
0.709 |
| HMC |
5 |
3.531 |
0.000994 |
1.401 |
| HMC |
10 |
3.393 |
0.00157 |
1.540 |
| HMC |
15 |
6.289 |
4.95e-07 |
5.501 |
| HMC |
30 |
4.738 |
4.45e-05 |
4.444 |
| SMC |
2 |
-1.193 |
0.238 |
-0.308 |
| SMC |
5 |
-0.353 |
0.725 |
-0.084 |
| SMC |
10 |
-0.840 |
0.404 |
-0.215 |
| SMC |
15 |
2.150 |
0.0366 |
0.741 |
| SMC |
30 |
-0.048 |
0.962 |
-0.011 |
| Metro |
2 |
5.167 |
1.38e-05 |
5.781 |
| Metro |
5 |
7.273 |
4.38e-08 |
11.049 |
| Metro |
10 |
6.922 |
1.23e-07 |
15.907 |
| Metro |
15 |
6.248 |
8.01e-07 |
33.356 |
| Metro |
30 |
6.802 |
1.79e-07 |
32.981 |
| DEMetro_Z |
2 |
2.830 |
0.00712 |
1.188 |
| DEMetro_Z |
5 |
4.847 |
3.88e-05 |
360.695 |
| DEMetro_Z |
10 |
14.938 |
3.74e-15 |
902.143 |
| DEMetro_Z |
15 |
17.641 |
4.78e-17 |
1355.747 |
| DEMetro_Z |
30 |
43.404 |
6.14e-28 |
1034.567 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-0.864
|
0.395
|
-0.158
|
| HMC_vs_DEMetro_Z |
1
|
-4.821
|
4.17e-05
|
-0.880
|
| HMC_vs_DEMetro_Z |
2
|
-14.938
|
3.74e-15
|
-2.727
|
| HMC_vs_DEMetro_Z |
3
|
-17.523
|
5.71e-17
|
-3.199
|
| HMC_vs_DEMetro_Z |
4
|
-43.197
|
7.07e-28
|
-7.887
|
| Metro_vs_SMC |
0
|
5.307
|
1.08e-05
|
0.969
|
| Metro_vs_SMC |
1
|
7.576
|
2.37e-08
|
1.383
|
| Metro_vs_SMC |
2
|
6.987
|
1.11e-07
|
1.276
|
| Metro_vs_SMC |
3
|
6.035
|
1.45e-06
|
1.102
|
| Metro_vs_SMC |
4
|
6.743
|
2.12e-07
|
1.231
|
| Metro_vs_DEMetro_Z |
0
|
4.227
|
0.000215
|
0.772
|
| Metro_vs_DEMetro_Z |
1
|
-4.693
|
5.94e-05
|
-0.857
|
| Metro_vs_DEMetro_Z |
2
|
-14.694
|
5.71e-15
|
-2.683
|
| Metro_vs_DEMetro_Z |
3
|
-17.244
|
8.75e-17
|
-3.148
|
| Metro_vs_DEMetro_Z |
4
|
-42.338
|
1.26e-27
|
-7.730
|
| HMC_vs_Metro |
0
|
-4.737
|
5.27e-05
|
-0.865
|
| HMC_vs_Metro |
1
|
-6.294
|
7.13e-07
|
-1.149
|
| HMC_vs_Metro |
2
|
-6.039
|
1.43e-06
|
-1.103
|
| HMC_vs_Metro |
3
|
-5.154
|
1.65e-05
|
-0.941
|
| HMC_vs_Metro |
4
|
-5.372
|
9.01e-06
|
-0.981
|
| HMC_vs_SMC |
0
|
2.448
|
0.0207
|
0.447
|
| HMC_vs_SMC |
1
|
3.913
|
0.000506
|
0.714
|
| HMC_vs_SMC |
2
|
3.732
|
0.000823
|
0.681
|
| HMC_vs_SMC |
3
|
5.140
|
1.72e-05
|
0.938
|
| HMC_vs_SMC |
4
|
4.793
|
4.5e-05
|
0.875
|
| DEMetro_Z_vs_SMC |
0
|
3.711
|
0.000872
|
0.678
|
| DEMetro_Z_vs_SMC |
1
|
4.846
|
3.89e-05
|
0.885
|
| DEMetro_Z_vs_SMC |
2
|
14.942
|
3.71e-15
|
2.728
|
| DEMetro_Z_vs_SMC |
3
|
17.630
|
4.86e-17
|
3.219
|
| DEMetro_Z_vs_SMC |
4
|
43.377
|
6.28e-28
|
7.919
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.030 |
0.022 |
0.012 |
0.709 |
| HMC |
5 |
0.032 |
0.017 |
0.011 |
1.401 |
| HMC |
10 |
0.038 |
0.020 |
0.012 |
1.540 |
| HMC |
15 |
0.059 |
0.016 |
0.008 |
5.501 |
| HMC |
30 |
0.068 |
0.018 |
0.011 |
4.444 |
| SMC |
2 |
0.018 |
0.022 |
0.012 |
-0.308 |
| SMC |
5 |
0.016 |
0.017 |
0.011 |
-0.084 |
| SMC |
10 |
0.018 |
0.020 |
0.012 |
-0.215 |
| SMC |
15 |
0.021 |
0.016 |
0.008 |
0.741 |
| SMC |
30 |
0.018 |
0.018 |
0.011 |
-0.011 |
| Metro |
2 |
0.089 |
0.022 |
0.012 |
5.781 |
| Metro |
5 |
0.142 |
0.017 |
0.011 |
11.049 |
| Metro |
10 |
0.205 |
0.020 |
0.012 |
15.907 |
| Metro |
15 |
0.280 |
0.016 |
0.008 |
33.356 |
| Metro |
30 |
0.385 |
0.018 |
0.011 |
32.981 |
| DEMetro_Z |
2 |
0.036 |
0.022 |
0.012 |
1.188 |
| DEMetro_Z |
5 |
4.100 |
0.017 |
0.011 |
360.695 |
| DEMetro_Z |
10 |
10.506 |
0.020 |
0.012 |
902.143 |
| DEMetro_Z |
15 |
10.780 |
0.016 |
0.008 |
1355.747 |
| DEMetro_Z |
30 |
11.512 |
0.018 |
0.011 |
1034.567 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
3.324 |
0.00171 |
1.172 |
| HMC |
5 |
2.711 |
0.00901 |
0.833 |
| HMC |
10 |
2.907 |
0.00641 |
1.935 |
| HMC |
15 |
3.428 |
0.00157 |
2.023 |
| HMC |
30 |
4.978 |
2.39e-05 |
5.804 |
| SMC |
2 |
2.197 |
0.0334 |
0.870 |
| SMC |
5 |
-0.587 |
0.56 |
-0.130 |
| SMC |
10 |
0.276 |
0.783 |
0.078 |
| SMC |
15 |
-0.806 |
0.424 |
-0.195 |
| SMC |
30 |
-0.764 |
0.448 |
-0.195 |
| Metro |
2 |
6.499 |
2.2e-07 |
4.593 |
| Metro |
5 |
4.934 |
2.52e-05 |
4.540 |
| Metro |
10 |
7.318 |
4.21e-08 |
14.961 |
| Metro |
15 |
5.265 |
1.16e-05 |
11.262 |
| Metro |
30 |
11.361 |
2.95e-12 |
28.858 |
| DEMetro_Z |
2 |
5.450 |
3.53e-06 |
2.863 |
| DEMetro_Z |
5 |
3.756 |
0.000773 |
993.211 |
| DEMetro_Z |
10 |
5.948 |
1.84e-06 |
1906.429 |
| DEMetro_Z |
15 |
9.478 |
2.2e-10 |
1198.219 |
| DEMetro_Z |
30 |
14.515 |
7.81e-15 |
1337.020 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
0.603
|
0.551
|
0.110
|
| HMC_vs_SMC |
1
|
3.547
|
0.00135
|
0.648
|
| HMC_vs_SMC |
2
|
2.614
|
0.014
|
0.477
|
| HMC_vs_SMC |
3
|
3.711
|
0.000872
|
0.678
|
| HMC_vs_SMC |
4
|
5.205
|
1.43e-05
|
0.950
|
| Metro_vs_DEMetro_Z |
0
|
2.060
|
0.0485
|
0.376
|
| Metro_vs_DEMetro_Z |
1
|
-3.739
|
0.000809
|
-0.683
|
| Metro_vs_DEMetro_Z |
2
|
-5.904
|
2.07e-06
|
-1.078
|
| Metro_vs_DEMetro_Z |
3
|
-9.392
|
2.68e-10
|
-1.715
|
| Metro_vs_DEMetro_Z |
4
|
-14.190
|
1.39e-14
|
-2.591
|
| HMC_vs_Metro |
0
|
-5.065
|
2.12e-05
|
-0.925
|
| HMC_vs_Metro |
1
|
-3.843
|
0.000611
|
-0.702
|
| HMC_vs_Metro |
2
|
-6.199
|
9.24e-07
|
-1.132
|
| HMC_vs_Metro |
3
|
-4.202
|
0.00023
|
-0.767
|
| HMC_vs_Metro |
4
|
-8.395
|
2.98e-09
|
-1.533
|
| HMC_vs_DEMetro_Z |
0
|
-2.673
|
0.0122
|
-0.488
|
| HMC_vs_DEMetro_Z |
1
|
-3.752
|
0.000781
|
-0.685
|
| HMC_vs_DEMetro_Z |
2
|
-5.940
|
1.88e-06
|
-1.085
|
| HMC_vs_DEMetro_Z |
3
|
-9.473
|
2.22e-10
|
-1.730
|
| HMC_vs_DEMetro_Z |
4
|
-14.448
|
8.81e-15
|
-2.638
|
| Metro_vs_SMC |
0
|
4.565
|
8.49e-05
|
0.833
|
| Metro_vs_SMC |
1
|
5.287
|
1.14e-05
|
0.965
|
| Metro_vs_SMC |
2
|
7.136
|
7.47e-08
|
1.303
|
| Metro_vs_SMC |
3
|
5.346
|
9.7e-06
|
0.976
|
| Metro_vs_SMC |
4
|
11.370
|
3.32e-12
|
2.076
|
| DEMetro_Z_vs_SMC |
0
|
3.805
|
0.000677
|
0.695
|
| DEMetro_Z_vs_SMC |
1
|
3.756
|
0.000773
|
0.686
|
| DEMetro_Z_vs_SMC |
2
|
5.949
|
1.83e-06
|
1.086
|
| DEMetro_Z_vs_SMC |
3
|
9.479
|
2.19e-10
|
1.731
|
| DEMetro_Z_vs_SMC |
4
|
14.525
|
7.69e-15
|
2.652
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.033 |
0.020 |
0.011 |
1.172 |
| HMC |
5 |
0.050 |
0.031 |
0.022 |
0.833 |
| HMC |
10 |
0.051 |
0.026 |
0.013 |
1.935 |
| HMC |
15 |
0.063 |
0.031 |
0.016 |
2.023 |
| HMC |
30 |
0.111 |
0.029 |
0.014 |
5.804 |
| SMC |
2 |
0.030 |
0.020 |
0.011 |
0.870 |
| SMC |
5 |
0.028 |
0.031 |
0.022 |
-0.130 |
| SMC |
10 |
0.027 |
0.026 |
0.013 |
0.078 |
| SMC |
15 |
0.028 |
0.031 |
0.016 |
-0.195 |
| SMC |
30 |
0.027 |
0.029 |
0.014 |
-0.195 |
| Metro |
2 |
0.071 |
0.020 |
0.011 |
4.593 |
| Metro |
5 |
0.132 |
0.031 |
0.022 |
4.540 |
| Metro |
10 |
0.216 |
0.026 |
0.013 |
14.961 |
| Metro |
15 |
0.210 |
0.031 |
0.016 |
11.262 |
| Metro |
30 |
0.437 |
0.029 |
0.014 |
28.858 |
| DEMetro_Z |
2 |
0.052 |
0.020 |
0.011 |
2.863 |
| DEMetro_Z |
5 |
22.139 |
0.031 |
0.022 |
993.211 |
| DEMetro_Z |
10 |
24.216 |
0.026 |
0.013 |
1906.429 |
| DEMetro_Z |
15 |
19.082 |
0.031 |
0.016 |
1198.219 |
| DEMetro_Z |
30 |
18.920 |
0.029 |
0.014 |
1337.020 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
2.393 |
0.0212 |
1.000 |
| HMC |
5 |
5.147 |
5.7e-06 |
1.967 |
| HMC |
10 |
5.978 |
6.2e-07 |
2.972 |
| HMC |
15 |
8.784 |
6.97e-10 |
9.461 |
| HMC |
30 |
6.699 |
1.83e-07 |
7.547 |
| SMC |
2 |
-0.156 |
0.877 |
-0.039 |
| SMC |
5 |
0.167 |
0.868 |
0.042 |
| SMC |
10 |
-0.271 |
0.788 |
-0.067 |
| SMC |
15 |
2.485 |
0.0168 |
0.967 |
| SMC |
30 |
-0.964 |
0.34 |
-0.218 |
| Metro |
2 |
6.355 |
5.11e-07 |
8.490 |
| Metro |
5 |
8.851 |
8e-10 |
15.225 |
| Metro |
10 |
8.594 |
1.71e-09 |
24.772 |
| Metro |
15 |
7.295 |
4.88e-08 |
54.532 |
| Metro |
30 |
9.668 |
1.38e-10 |
52.166 |
| DEMetro_Z |
2 |
6.600 |
5.52e-08 |
2.768 |
| DEMetro_Z |
5 |
5.304 |
1.09e-05 |
481.155 |
| DEMetro_Z |
10 |
14.662 |
6.04e-15 |
1347.942 |
| DEMetro_Z |
15 |
18.202 |
2.07e-17 |
2195.599 |
| DEMetro_Z |
30 |
41.433 |
2.32e-27 |
1422.451 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
4.413
|
0.000129
|
0.806
|
| Metro_vs_DEMetro_Z |
1
|
-5.135
|
1.74e-05
|
-0.938
|
| Metro_vs_DEMetro_Z |
2
|
-14.408
|
9.45e-15
|
-2.631
|
| Metro_vs_DEMetro_Z |
3
|
-17.782
|
3.87e-17
|
-3.247
|
| Metro_vs_DEMetro_Z |
4
|
-39.800
|
7.32e-27
|
-7.267
|
| DEMetro_Z_vs_SMC |
0
|
7.078
|
8.7e-08
|
1.292
|
| DEMetro_Z_vs_SMC |
1
|
5.302
|
1.1e-05
|
0.968
|
| DEMetro_Z_vs_SMC |
2
|
14.662
|
6.04e-15
|
2.677
|
| DEMetro_Z_vs_SMC |
3
|
18.191
|
2.11e-17
|
3.321
|
| DEMetro_Z_vs_SMC |
4
|
41.463
|
2.28e-27
|
7.570
|
| HMC_vs_DEMetro_Z |
0
|
-3.611
|
0.00114
|
-0.659
|
| HMC_vs_DEMetro_Z |
1
|
-5.276
|
1.18e-05
|
-0.963
|
| HMC_vs_DEMetro_Z |
2
|
-14.644
|
6.24e-15
|
-2.674
|
| HMC_vs_DEMetro_Z |
3
|
-18.099
|
2.42e-17
|
-3.304
|
| HMC_vs_DEMetro_Z |
4
|
-41.218
|
2.7e-27
|
-7.525
|
| HMC_vs_Metro |
0
|
-5.773
|
2.97e-06
|
-1.054
|
| HMC_vs_Metro |
1
|
-7.878
|
1.09e-08
|
-1.438
|
| HMC_vs_Metro |
2
|
-7.107
|
8.06e-08
|
-1.298
|
| HMC_vs_Metro |
3
|
-5.946
|
1.85e-06
|
-1.086
|
| HMC_vs_Metro |
4
|
-7.570
|
2.4e-08
|
-1.382
|
| HMC_vs_SMC |
0
|
2.579
|
0.0153
|
0.471
|
| HMC_vs_SMC |
1
|
5.112
|
1.86e-05
|
0.933
|
| HMC_vs_SMC |
2
|
5.582
|
5.04e-06
|
1.019
|
| HMC_vs_SMC |
3
|
7.910
|
1.01e-08
|
1.444
|
| HMC_vs_SMC |
4
|
6.832
|
1.67e-07
|
1.247
|
| Metro_vs_SMC |
0
|
6.328
|
6.5e-07
|
1.155
|
| Metro_vs_SMC |
1
|
8.854
|
9.68e-10
|
1.616
|
| Metro_vs_SMC |
2
|
8.667
|
1.52e-09
|
1.582
|
| Metro_vs_SMC |
3
|
7.142
|
7.36e-08
|
1.304
|
| Metro_vs_SMC |
4
|
9.637
|
1.52e-10
|
1.759
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.036 |
0.028 |
0.008 |
1.000 |
| HMC |
5 |
0.039 |
0.024 |
0.007 |
1.967 |
| HMC |
10 |
0.045 |
0.025 |
0.007 |
2.972 |
| HMC |
15 |
0.062 |
0.023 |
0.004 |
9.461 |
| HMC |
30 |
0.076 |
0.025 |
0.007 |
7.547 |
| SMC |
2 |
0.028 |
0.028 |
0.008 |
-0.039 |
| SMC |
5 |
0.024 |
0.024 |
0.007 |
0.042 |
| SMC |
10 |
0.025 |
0.025 |
0.007 |
-0.067 |
| SMC |
15 |
0.027 |
0.023 |
0.004 |
0.967 |
| SMC |
30 |
0.023 |
0.025 |
0.007 |
-0.218 |
| Metro |
2 |
0.093 |
0.028 |
0.008 |
8.490 |
| Metro |
5 |
0.137 |
0.024 |
0.007 |
15.225 |
| Metro |
10 |
0.194 |
0.025 |
0.007 |
24.772 |
| Metro |
15 |
0.249 |
0.023 |
0.004 |
54.532 |
| Metro |
30 |
0.375 |
0.025 |
0.007 |
52.166 |
| DEMetro_Z |
2 |
0.049 |
0.028 |
0.008 |
2.768 |
| DEMetro_Z |
5 |
3.593 |
0.024 |
0.007 |
481.155 |
| DEMetro_Z |
10 |
9.217 |
0.025 |
0.007 |
1347.942 |
| DEMetro_Z |
15 |
9.110 |
0.023 |
0.004 |
2195.599 |
| DEMetro_Z |
30 |
9.575 |
0.025 |
0.007 |
1422.451 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
2.367 |
0.0225 |
0.947 |
| HMC |
5 |
4.747 |
1.47e-05 |
1.361 |
| HMC |
10 |
6.393 |
1.77e-07 |
3.256 |
| HMC |
15 |
8.825 |
3.73e-10 |
6.644 |
| HMC |
30 |
6.955 |
6.36e-08 |
5.216 |
| SMC |
2 |
0.123 |
0.902 |
0.031 |
| SMC |
5 |
-0.650 |
0.519 |
-0.143 |
| SMC |
10 |
0.358 |
0.721 |
0.102 |
| SMC |
15 |
1.836 |
0.0726 |
0.642 |
| SMC |
30 |
-1.535 |
0.131 |
-0.324 |
| Metro |
2 |
7.326 |
3.13e-08 |
7.668 |
| Metro |
5 |
9.607 |
9.93e-11 |
11.241 |
| Metro |
10 |
8.921 |
7.63e-10 |
24.791 |
| Metro |
15 |
8.319 |
3.52e-09 |
41.637 |
| Metro |
30 |
11.560 |
2.08e-12 |
40.873 |
| DEMetro_Z |
2 |
6.481 |
5.37e-08 |
2.377 |
| DEMetro_Z |
5 |
10.818 |
1.06e-11 |
80.378 |
| DEMetro_Z |
10 |
40.183 |
5.01e-27 |
212.181 |
| DEMetro_Z |
15 |
75.036 |
6.69e-35 |
277.792 |
| DEMetro_Z |
30 |
63.518 |
6.08e-33 |
161.317 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
7.225
|
5.9e-08
|
1.319
|
| DEMetro_Z_vs_SMC |
1
|
10.808
|
1.1e-11
|
1.973
|
| DEMetro_Z_vs_SMC |
2
|
39.918
|
6.73e-27
|
7.288
|
| DEMetro_Z_vs_SMC |
3
|
74.724
|
1.02e-34
|
13.643
|
| DEMetro_Z_vs_SMC |
4
|
63.878
|
9.41e-33
|
11.663
|
| HMC_vs_Metro |
0
|
-6.931
|
1.28e-07
|
-1.265
|
| HMC_vs_Metro |
1
|
-9.027
|
6.38e-10
|
-1.648
|
| HMC_vs_Metro |
2
|
-7.255
|
5.47e-08
|
-1.324
|
| HMC_vs_Metro |
3
|
-7.063
|
9.06e-08
|
-1.289
|
| HMC_vs_Metro |
4
|
-9.408
|
2.59e-10
|
-1.718
|
| Metro_vs_DEMetro_Z |
0
|
4.981
|
2.67e-05
|
0.909
|
| Metro_vs_DEMetro_Z |
1
|
-9.601
|
1.65e-10
|
-1.753
|
| Metro_vs_DEMetro_Z |
2
|
-33.795
|
7.63e-25
|
-6.170
|
| Metro_vs_DEMetro_Z |
3
|
-41.455
|
2.29e-27
|
-7.569
|
| Metro_vs_DEMetro_Z |
4
|
-30.324
|
1.63e-23
|
-5.536
|
| HMC_vs_SMC |
0
|
2.503
|
0.0182
|
0.457
|
| HMC_vs_SMC |
1
|
5.982
|
1.67e-06
|
1.092
|
| HMC_vs_SMC |
2
|
5.208
|
1.42e-05
|
0.951
|
| HMC_vs_SMC |
3
|
8.170
|
5.22e-09
|
1.492
|
| HMC_vs_SMC |
4
|
7.397
|
3.77e-08
|
1.350
|
| Metro_vs_SMC |
0
|
7.381
|
3.93e-08
|
1.348
|
| Metro_vs_SMC |
1
|
9.640
|
1.51e-10
|
1.760
|
| Metro_vs_SMC |
2
|
8.873
|
9.25e-10
|
1.620
|
| Metro_vs_SMC |
3
|
8.272
|
4.05e-09
|
1.510
|
| Metro_vs_SMC |
4
|
11.524
|
2.4e-12
|
2.104
|
| HMC_vs_DEMetro_Z |
0
|
-3.385
|
0.00206
|
-0.618
|
| HMC_vs_DEMetro_Z |
1
|
-10.555
|
1.91e-11
|
-1.927
|
| HMC_vs_DEMetro_Z |
2
|
-40.139
|
5.75e-27
|
-7.328
|
| HMC_vs_DEMetro_Z |
3
|
-68.426
|
1.3e-33
|
-12.493
|
| HMC_vs_DEMetro_Z |
4
|
-55.312
|
5.92e-31
|
-10.098
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.019 |
0.014 |
0.005 |
0.947 |
| HMC |
5 |
0.022 |
0.014 |
0.006 |
1.361 |
| HMC |
10 |
0.028 |
0.014 |
0.004 |
3.256 |
| HMC |
15 |
0.036 |
0.014 |
0.003 |
6.644 |
| HMC |
30 |
0.045 |
0.015 |
0.006 |
5.216 |
| SMC |
2 |
0.015 |
0.014 |
0.005 |
0.031 |
| SMC |
5 |
0.013 |
0.014 |
0.006 |
-0.143 |
| SMC |
10 |
0.014 |
0.014 |
0.004 |
0.102 |
| SMC |
15 |
0.016 |
0.014 |
0.003 |
0.642 |
| SMC |
30 |
0.013 |
0.015 |
0.006 |
-0.324 |
| Metro |
2 |
0.050 |
0.014 |
0.005 |
7.668 |
| Metro |
5 |
0.084 |
0.014 |
0.006 |
11.241 |
| Metro |
10 |
0.122 |
0.014 |
0.004 |
24.791 |
| Metro |
15 |
0.155 |
0.014 |
0.003 |
41.637 |
| Metro |
30 |
0.253 |
0.015 |
0.006 |
40.873 |
| DEMetro_Z |
2 |
0.025 |
0.014 |
0.005 |
2.377 |
| DEMetro_Z |
5 |
0.516 |
0.014 |
0.006 |
80.378 |
| DEMetro_Z |
10 |
0.942 |
0.014 |
0.004 |
212.181 |
| DEMetro_Z |
15 |
0.954 |
0.014 |
0.003 |
277.792 |
| DEMetro_Z |
30 |
0.952 |
0.015 |
0.006 |
161.317 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
KDE + Init Plots
Trace Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Vary_Dimension_with_heavy_Tails
(MvStudentT,
dimension,
30 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
0.274 |
0.785 |
0.074 |
| HMC |
5 |
1.682 |
0.0984 |
0.512 |
| HMC |
10 |
1.495 |
0.146 |
2.917 |
| HMC |
15 |
1.396 |
0.169 |
0.478 |
| HMC |
30 |
1.440 |
0.161 |
16.644 |
| SMC |
2 |
3.170 |
0.0025 |
0.938 |
| SMC |
5 |
10.453 |
2.27e-11 |
39.706 |
| SMC |
10 |
19.912 |
1.63e-18 |
72.996 |
| SMC |
15 |
29.449 |
9.58e-25 |
24.270 |
| SMC |
30 |
54.838 |
3.99e-31 |
129.468 |
| Metro |
2 |
2.224 |
0.0322 |
1.110 |
| Metro |
5 |
3.406 |
0.0018 |
2.845 |
| Metro |
10 |
8.570 |
6.56e-10 |
6.112 |
| Metro |
15 |
6.137 |
2.65e-07 |
2.611 |
| Metro |
30 |
6.923 |
1.26e-07 |
20.035 |
| DEMetro_Z |
2 |
3.167 |
0.00282 |
1.272 |
| DEMetro_Z |
5 |
6.625 |
2.91e-07 |
150.211 |
| DEMetro_Z |
10 |
13.335 |
6.67e-14 |
229.867 |
| DEMetro_Z |
15 |
17.727 |
3.85e-17 |
74.479 |
| DEMetro_Z |
30 |
22.869 |
4.2e-20 |
481.992 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-2.840
|
0.00816
|
-0.519
|
| HMC_vs_DEMetro_Z |
1
|
-6.623
|
2.93e-07
|
-1.209
|
| HMC_vs_DEMetro_Z |
2
|
-13.563
|
4.37e-14
|
-2.476
|
| HMC_vs_DEMetro_Z |
3
|
-17.420
|
6.68e-17
|
-3.180
|
| HMC_vs_DEMetro_Z |
4
|
-19.616
|
2.77e-18
|
-3.581
|
| Metro_vs_SMC |
0
|
0.345
|
0.733
|
0.063
|
| Metro_vs_SMC |
1
|
-9.745
|
1.18e-10
|
-1.779
|
| Metro_vs_SMC |
2
|
-17.302
|
8.01e-17
|
-3.159
|
| Metro_vs_SMC |
3
|
-28.711
|
7.54e-23
|
-5.242
|
| Metro_vs_SMC |
4
|
-27.598
|
2.28e-22
|
-5.039
|
| Metro_vs_DEMetro_Z |
0
|
-0.253
|
0.802
|
-0.046
|
| Metro_vs_DEMetro_Z |
1
|
-6.486
|
4.24e-07
|
-1.184
|
| Metro_vs_DEMetro_Z |
2
|
-13.144
|
9.61e-14
|
-2.400
|
| Metro_vs_DEMetro_Z |
3
|
-16.922
|
1.44e-16
|
-3.090
|
| Metro_vs_DEMetro_Z |
4
|
-21.929
|
1.33e-19
|
-4.004
|
| HMC_vs_Metro |
0
|
-1.925
|
0.064
|
-0.352
|
| HMC_vs_Metro |
1
|
-2.700
|
0.0115
|
-0.493
|
| HMC_vs_Metro |
2
|
-1.578
|
0.126
|
-0.288
|
| HMC_vs_Metro |
3
|
-6.203
|
9.15e-07
|
-1.132
|
| HMC_vs_Metro |
4
|
-0.273
|
0.787
|
-0.050
|
| HMC_vs_SMC |
0
|
-4.037
|
0.000362
|
-0.737
|
| HMC_vs_SMC |
1
|
-10.314
|
3.26e-11
|
-1.883
|
| HMC_vs_SMC |
2
|
-16.135
|
5.05e-16
|
-2.946
|
| HMC_vs_SMC |
3
|
-28.587
|
8.52e-23
|
-5.219
|
| HMC_vs_SMC |
4
|
-9.532
|
1.93e-10
|
-1.740
|
| DEMetro_Z_vs_SMC |
0
|
0.764
|
0.451
|
0.140
|
| DEMetro_Z_vs_SMC |
1
|
4.636
|
6.96e-05
|
0.846
|
| DEMetro_Z_vs_SMC |
2
|
8.686
|
1.46e-09
|
1.586
|
| DEMetro_Z_vs_SMC |
3
|
11.903
|
1.1e-12
|
2.173
|
| DEMetro_Z_vs_SMC |
4
|
16.166
|
4.8e-16
|
2.952
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.068 |
0.065 |
0.042 |
0.074 |
| HMC |
5 |
0.074 |
0.064 |
0.020 |
0.512 |
| HMC |
10 |
0.104 |
0.061 |
0.015 |
2.917 |
| HMC |
15 |
0.099 |
0.073 |
0.054 |
0.478 |
| HMC |
30 |
0.327 |
0.064 |
0.016 |
16.644 |
| SMC |
2 |
0.104 |
0.065 |
0.042 |
0.938 |
| SMC |
5 |
0.865 |
0.064 |
0.020 |
39.706 |
| SMC |
10 |
1.143 |
0.061 |
0.015 |
72.996 |
| SMC |
15 |
1.381 |
0.073 |
0.054 |
24.270 |
| SMC |
30 |
2.110 |
0.064 |
0.016 |
129.468 |
| Metro |
2 |
0.111 |
0.065 |
0.042 |
1.110 |
| Metro |
5 |
0.121 |
0.064 |
0.020 |
2.845 |
| Metro |
10 |
0.152 |
0.061 |
0.015 |
6.112 |
| Metro |
15 |
0.214 |
0.073 |
0.054 |
2.611 |
| Metro |
30 |
0.381 |
0.064 |
0.016 |
20.035 |
| DEMetro_Z |
2 |
0.118 |
0.065 |
0.042 |
1.272 |
| DEMetro_Z |
5 |
3.097 |
0.064 |
0.020 |
150.211 |
| DEMetro_Z |
10 |
3.469 |
0.061 |
0.015 |
229.867 |
| DEMetro_Z |
15 |
4.088 |
0.073 |
0.054 |
74.479 |
| DEMetro_Z |
30 |
7.680 |
0.064 |
0.016 |
481.992 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
-1.263 |
0.213 |
-0.261 |
| HMC |
5 |
-1.272 |
0.209 |
-0.301 |
| HMC |
10 |
0.382 |
0.704 |
0.129 |
| HMC |
15 |
-1.057 |
0.299 |
-0.193 |
| HMC |
30 |
1.075 |
0.291 |
368.475 |
| SMC |
2 |
1.444 |
0.155 |
0.306 |
| SMC |
5 |
37.872 |
1.97e-26 |
98.791 |
| SMC |
10 |
77.673 |
2.66e-35 |
333.745 |
| SMC |
15 |
62.168 |
2.42e-54 |
16.958 |
| SMC |
30 |
216.976 |
2.37e-48 |
732.009 |
| Metro |
2 |
-1.559 |
0.127 |
-0.308 |
| Metro |
5 |
-1.566 |
0.124 |
-0.327 |
| Metro |
10 |
-0.446 |
0.657 |
-0.099 |
| Metro |
15 |
-0.749 |
0.459 |
-0.138 |
| Metro |
30 |
3.096 |
0.00431 |
12.511 |
| DEMetro_Z |
2 |
-1.544 |
0.132 |
-0.294 |
| DEMetro_Z |
5 |
4.989 |
2.61e-05 |
61.426 |
| DEMetro_Z |
10 |
8.231 |
4.46e-09 |
88.169 |
| DEMetro_Z |
15 |
8.211 |
3.15e-10 |
3.497 |
| DEMetro_Z |
30 |
17.668 |
4.54e-17 |
204.927 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
-3.550
|
0.00134
|
-0.648
|
| HMC_vs_SMC |
1
|
-38.572
|
1.79e-26
|
-7.042
|
| HMC_vs_SMC |
2
|
-76.849
|
4.55e-35
|
-14.031
|
| HMC_vs_SMC |
3
|
-84.772
|
2.68e-36
|
-15.477
|
| HMC_vs_SMC |
4
|
-1.060
|
0.298
|
-0.194
|
| Metro_vs_DEMetro_Z |
0
|
-0.235
|
0.816
|
-0.043
|
| Metro_vs_DEMetro_Z |
1
|
-5.028
|
2.34e-05
|
-0.918
|
| Metro_vs_DEMetro_Z |
2
|
-8.240
|
4.39e-09
|
-1.504
|
| Metro_vs_DEMetro_Z |
3
|
-9.522
|
1.98e-10
|
-1.738
|
| Metro_vs_DEMetro_Z |
4
|
-14.624
|
6.45e-15
|
-2.670
|
| HMC_vs_Metro |
0
|
0.458
|
0.651
|
0.084
|
| HMC_vs_Metro |
1
|
0.199
|
0.844
|
0.036
|
| HMC_vs_Metro |
2
|
0.809
|
0.425
|
0.148
|
| HMC_vs_Metro |
3
|
-2.661
|
0.0126
|
-0.486
|
| HMC_vs_Metro |
4
|
1.037
|
0.308
|
0.189
|
| HMC_vs_DEMetro_Z |
0
|
0.398
|
0.693
|
0.073
|
| HMC_vs_DEMetro_Z |
1
|
-5.019
|
2.41e-05
|
-0.916
|
| HMC_vs_DEMetro_Z |
2
|
-8.242
|
4.37e-09
|
-1.505
|
| HMC_vs_DEMetro_Z |
3
|
-9.605
|
1.63e-10
|
-1.754
|
| HMC_vs_DEMetro_Z |
4
|
0.476
|
0.638
|
0.087
|
| Metro_vs_SMC |
0
|
-4.340
|
0.000158
|
-0.792
|
| Metro_vs_SMC |
1
|
-38.459
|
1.94e-26
|
-7.022
|
| Metro_vs_SMC |
2
|
-77.617
|
3.42e-35
|
-14.171
|
| Metro_vs_SMC |
3
|
-85.123
|
2.38e-36
|
-15.541
|
| Metro_vs_SMC |
4
|
-115.954
|
3.12e-40
|
-21.170
|
| DEMetro_Z_vs_SMC |
0
|
-4.653
|
6.65e-05
|
-0.849
|
| DEMetro_Z_vs_SMC |
1
|
-3.056
|
0.00479
|
-0.558
|
| DEMetro_Z_vs_SMC |
2
|
-19.357
|
3.97e-18
|
-3.534
|
| DEMetro_Z_vs_SMC |
3
|
-30.983
|
8.87e-24
|
-5.657
|
| DEMetro_Z_vs_SMC |
4
|
-44.721
|
2.62e-28
|
-8.165
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
5.393 |
9.112 |
14.240 |
-0.261 |
| HMC |
5 |
5.929 |
8.258 |
7.752 |
-0.301 |
| HMC |
10 |
6.646 |
5.887 |
5.869 |
0.129 |
| HMC |
15 |
5.482 |
33.673 |
146.019 |
-0.193 |
| HMC |
30 |
1517.615 |
5.303 |
4.104 |
368.475 |
| SMC |
2 |
13.466 |
9.112 |
14.240 |
0.306 |
| SMC |
5 |
774.082 |
8.258 |
7.752 |
98.791 |
| SMC |
10 |
1964.573 |
5.887 |
5.869 |
333.745 |
| SMC |
15 |
2509.819 |
33.673 |
146.019 |
16.958 |
| SMC |
30 |
3009.650 |
5.303 |
4.104 |
732.009 |
| Metro |
2 |
4.722 |
9.112 |
14.240 |
-0.308 |
| Metro |
5 |
5.721 |
8.258 |
7.752 |
-0.327 |
| Metro |
10 |
5.308 |
5.887 |
5.869 |
-0.099 |
| Metro |
15 |
13.538 |
33.673 |
146.019 |
-0.138 |
| Metro |
30 |
56.650 |
5.303 |
4.104 |
12.511 |
| DEMetro_Z |
2 |
4.919 |
9.112 |
14.240 |
-0.294 |
| DEMetro_Z |
5 |
484.431 |
8.258 |
7.752 |
61.426 |
| DEMetro_Z |
10 |
523.337 |
5.887 |
5.869 |
88.169 |
| DEMetro_Z |
15 |
544.313 |
33.673 |
146.019 |
3.497 |
| DEMetro_Z |
30 |
846.376 |
5.303 |
4.104 |
204.927 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
1.728 |
0.0896 |
0.504 |
| HMC |
5 |
3.708 |
0.00068 |
1.918 |
| HMC |
10 |
2.074 |
0.047 |
9.677 |
| HMC |
15 |
3.911 |
0.000441 |
3.006 |
| HMC |
30 |
1.546 |
0.133 |
111.810 |
| SMC |
2 |
11.540 |
1.65e-12 |
18.687 |
| SMC |
5 |
58.057 |
1.44e-31 |
797.447 |
| SMC |
10 |
135.774 |
3.16e-42 |
1946.292 |
| SMC |
15 |
156.557 |
4.06e-44 |
735.400 |
| SMC |
30 |
411.661 |
2.82e-56 |
2362.188 |
| Metro |
2 |
5.809 |
1.02e-06 |
2.831 |
| Metro |
5 |
6.677 |
1.52e-07 |
5.386 |
| Metro |
10 |
9.721 |
7.7e-11 |
11.596 |
| Metro |
15 |
4.962 |
2.73e-05 |
11.545 |
| Metro |
30 |
7.245 |
5.59e-08 |
101.214 |
| DEMetro_Z |
2 |
9.384 |
1.13e-11 |
4.196 |
| DEMetro_Z |
5 |
7.398 |
3.76e-08 |
347.088 |
| DEMetro_Z |
10 |
17.014 |
1.25e-16 |
736.254 |
| DEMetro_Z |
15 |
18.692 |
1.01e-17 |
286.270 |
| DEMetro_Z |
30 |
35.280 |
2.25e-25 |
1159.241 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-2.450
|
0.0205
|
-0.447
|
| Metro_vs_DEMetro_Z |
1
|
-7.298
|
4.88e-08
|
-1.332
|
| Metro_vs_DEMetro_Z |
2
|
-16.895
|
1.5e-16
|
-3.085
|
| Metro_vs_DEMetro_Z |
3
|
-18.277
|
1.86e-17
|
-3.337
|
| Metro_vs_DEMetro_Z |
4
|
-28.069
|
1.42e-22
|
-5.125
|
| DEMetro_Z_vs_SMC |
0
|
-8.498
|
2.31e-09
|
-1.552
|
| DEMetro_Z_vs_SMC |
1
|
-9.863
|
9.02e-11
|
-1.801
|
| DEMetro_Z_vs_SMC |
2
|
-24.675
|
5.16e-21
|
-4.505
|
| DEMetro_Z_vs_SMC |
3
|
-27.013
|
4.15e-22
|
-4.932
|
| DEMetro_Z_vs_SMC |
4
|
-36.723
|
7.23e-26
|
-6.705
|
| HMC_vs_DEMetro_Z |
0
|
-9.243
|
3.82e-10
|
-1.687
|
| HMC_vs_DEMetro_Z |
1
|
-7.362
|
4.13e-08
|
-1.344
|
| HMC_vs_DEMetro_Z |
2
|
-17.307
|
7.94e-17
|
-3.160
|
| HMC_vs_DEMetro_Z |
3
|
-18.490
|
1.36e-17
|
-3.376
|
| HMC_vs_DEMetro_Z |
4
|
-13.574
|
4.29e-14
|
-2.478
|
| HMC_vs_Metro |
0
|
-4.448
|
0.000117
|
-0.812
|
| HMC_vs_Metro |
1
|
-4.035
|
0.000364
|
-0.737
|
| HMC_vs_Metro |
2
|
-0.413
|
0.683
|
-0.075
|
| HMC_vs_Metro |
3
|
-4.239
|
0.000208
|
-0.774
|
| HMC_vs_Metro |
4
|
0.140
|
0.89
|
0.026
|
| HMC_vs_SMC |
0
|
-11.210
|
4.65e-12
|
-2.047
|
| HMC_vs_SMC |
1
|
-58.075
|
1.46e-31
|
-10.603
|
| HMC_vs_SMC |
2
|
-128.213
|
1.7e-41
|
-23.408
|
| HMC_vs_SMC |
3
|
-151.190
|
1.44e-43
|
-27.603
|
| HMC_vs_SMC |
4
|
-30.815
|
1.03e-23
|
-5.626
|
| Metro_vs_SMC |
0
|
-9.129
|
5e-10
|
-1.667
|
| Metro_vs_SMC |
1
|
-58.011
|
1.51e-31
|
-10.591
|
| Metro_vs_SMC |
2
|
-133.374
|
5.43e-42
|
-24.351
|
| Metro_vs_SMC |
3
|
-142.973
|
7.26e-43
|
-26.103
|
| Metro_vs_SMC |
4
|
-132.688
|
6.3e-42
|
-24.225
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.141 |
0.124 |
0.035 |
0.504 |
| HMC |
5 |
0.166 |
0.122 |
0.023 |
1.918 |
| HMC |
10 |
0.281 |
0.117 |
0.017 |
9.677 |
| HMC |
15 |
0.286 |
0.131 |
0.052 |
3.006 |
| HMC |
30 |
2.108 |
0.117 |
0.018 |
111.810 |
| SMC |
2 |
0.777 |
0.124 |
0.035 |
18.687 |
| SMC |
5 |
18.377 |
0.122 |
0.023 |
797.447 |
| SMC |
10 |
33.031 |
0.117 |
0.017 |
1946.292 |
| SMC |
15 |
38.058 |
0.131 |
0.052 |
735.400 |
| SMC |
30 |
42.165 |
0.117 |
0.018 |
2362.188 |
| Metro |
2 |
0.223 |
0.124 |
0.035 |
2.831 |
| Metro |
5 |
0.246 |
0.122 |
0.023 |
5.386 |
| Metro |
10 |
0.313 |
0.117 |
0.017 |
11.596 |
| Metro |
15 |
0.726 |
0.131 |
0.052 |
11.545 |
| Metro |
30 |
1.919 |
0.117 |
0.018 |
101.214 |
| DEMetro_Z |
2 |
0.271 |
0.124 |
0.035 |
4.196 |
| DEMetro_Z |
5 |
8.067 |
0.122 |
0.023 |
347.088 |
| DEMetro_Z |
10 |
12.568 |
0.117 |
0.017 |
736.254 |
| DEMetro_Z |
15 |
14.895 |
0.131 |
0.052 |
286.270 |
| DEMetro_Z |
30 |
20.752 |
0.117 |
0.018 |
1159.241 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
2.577 |
0.0126 |
0.622 |
| HMC |
5 |
2.833 |
0.00811 |
3.416 |
| HMC |
10 |
3.410 |
0.00192 |
11.982 |
| HMC |
15 |
4.879 |
3.52e-05 |
19.460 |
| HMC |
30 |
5.326 |
1.02e-05 |
31.396 |
| SMC |
2 |
15.858 |
5.19e-16 |
28.421 |
| SMC |
5 |
135.948 |
9.59e-44 |
169.340 |
| SMC |
10 |
112.025 |
1.51e-40 |
190.649 |
| SMC |
15 |
157.935 |
1.23e-45 |
201.511 |
| SMC |
30 |
195.178 |
7.43e-50 |
182.632 |
| Metro |
2 |
8.438 |
2.83e-10 |
4.082 |
| Metro |
5 |
12.179 |
8.38e-14 |
8.494 |
| Metro |
10 |
9.311 |
2.83e-10 |
20.141 |
| Metro |
15 |
7.836 |
1.2e-08 |
45.706 |
| Metro |
30 |
11.869 |
1.17e-12 |
92.345 |
| DEMetro_Z |
2 |
9.159 |
1.18e-10 |
6.149 |
| DEMetro_Z |
5 |
19.172 |
4.97e-18 |
131.204 |
| DEMetro_Z |
10 |
74.572 |
6.43e-35 |
210.492 |
| DEMetro_Z |
15 |
70.838 |
3.26e-34 |
230.853 |
| DEMetro_Z |
30 |
82.076 |
3.77e-36 |
222.806 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
-11.162
|
5.15e-12
|
-2.038
|
| DEMetro_Z_vs_SMC |
1
|
-5.515
|
6.07e-06
|
-1.007
|
| DEMetro_Z_vs_SMC |
2
|
6.305
|
6.93e-07
|
1.151
|
| DEMetro_Z_vs_SMC |
3
|
8.871
|
9.28e-10
|
1.620
|
| DEMetro_Z_vs_SMC |
4
|
14.048
|
1.8e-14
|
2.565
|
| HMC_vs_Metro |
0
|
-7.200
|
6.31e-08
|
-1.315
|
| HMC_vs_Metro |
1
|
-4.040
|
0.000358
|
-0.738
|
| HMC_vs_Metro |
2
|
-1.902
|
0.0672
|
-0.347
|
| HMC_vs_Metro |
3
|
-4.430
|
0.000123
|
-0.809
|
| HMC_vs_Metro |
4
|
-5.908
|
2.05e-06
|
-1.079
|
| Metro_vs_DEMetro_Z |
0
|
-2.476
|
0.0194
|
-0.452
|
| Metro_vs_DEMetro_Z |
1
|
-18.286
|
1.83e-17
|
-3.339
|
| Metro_vs_DEMetro_Z |
2
|
-54.215
|
1.05e-30
|
-9.898
|
| Metro_vs_DEMetro_Z |
3
|
-31.872
|
3.99e-24
|
-5.819
|
| Metro_vs_DEMetro_Z |
4
|
-14.926
|
3.81e-15
|
-2.725
|
| HMC_vs_SMC |
0
|
-15.617
|
1.18e-15
|
-2.851
|
| HMC_vs_SMC |
1
|
-98.216
|
3.8e-38
|
-17.932
|
| HMC_vs_SMC |
2
|
-46.081
|
1.11e-28
|
-8.413
|
| HMC_vs_SMC |
3
|
-43.979
|
4.23e-28
|
-8.030
|
| HMC_vs_SMC |
4
|
-25.132
|
3.1e-21
|
-4.588
|
| Metro_vs_SMC |
0
|
-12.998
|
1.27e-13
|
-2.373
|
| Metro_vs_SMC |
1
|
-114.396
|
4.62e-40
|
-20.886
|
| Metro_vs_SMC |
2
|
-61.304
|
3.07e-32
|
-11.193
|
| Metro_vs_SMC |
3
|
-27.216
|
3.37e-22
|
-4.969
|
| Metro_vs_SMC |
4
|
-11.663
|
1.8e-12
|
-2.129
|
| HMC_vs_DEMetro_Z |
0
|
-8.238
|
4.4e-09
|
-1.504
|
| HMC_vs_DEMetro_Z |
1
|
-18.826
|
8.41e-18
|
-3.437
|
| HMC_vs_DEMetro_Z |
2
|
-46.488
|
8.66e-29
|
-8.488
|
| HMC_vs_DEMetro_Z |
3
|
-40.121
|
5.82e-27
|
-7.325
|
| HMC_vs_DEMetro_Z |
4
|
-29.982
|
2.24e-23
|
-5.474
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.018 |
0.015 |
0.005 |
0.622 |
| HMC |
5 |
0.024 |
0.015 |
0.003 |
3.416 |
| HMC |
10 |
0.043 |
0.015 |
0.002 |
11.982 |
| HMC |
15 |
0.056 |
0.015 |
0.002 |
19.460 |
| HMC |
30 |
0.083 |
0.016 |
0.002 |
31.396 |
| SMC |
2 |
0.144 |
0.015 |
0.005 |
28.421 |
| SMC |
5 |
0.501 |
0.015 |
0.003 |
169.340 |
| SMC |
10 |
0.455 |
0.015 |
0.002 |
190.649 |
| SMC |
15 |
0.432 |
0.015 |
0.002 |
201.511 |
| SMC |
30 |
0.409 |
0.016 |
0.002 |
182.632 |
| Metro |
2 |
0.033 |
0.015 |
0.005 |
4.082 |
| Metro |
5 |
0.039 |
0.015 |
0.003 |
8.494 |
| Metro |
10 |
0.062 |
0.015 |
0.002 |
20.141 |
| Metro |
15 |
0.110 |
0.015 |
0.002 |
45.706 |
| Metro |
30 |
0.214 |
0.016 |
0.002 |
92.345 |
| DEMetro_Z |
2 |
0.043 |
0.015 |
0.005 |
6.149 |
| DEMetro_Z |
5 |
0.391 |
0.015 |
0.003 |
131.204 |
| DEMetro_Z |
10 |
0.500 |
0.015 |
0.002 |
210.492 |
| DEMetro_Z |
15 |
0.492 |
0.015 |
0.002 |
230.853 |
| DEMetro_Z |
30 |
0.495 |
0.016 |
0.002 |
222.806 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
0.306 |
0.76 |
0.085 |
| HMC |
5 |
0.511 |
0.612 |
0.294 |
| HMC |
10 |
1.242 |
0.224 |
2.880 |
| HMC |
15 |
1.151 |
0.259 |
5.500 |
| HMC |
30 |
2.090 |
0.0452 |
2.994 |
| SMC |
2 |
1.229 |
0.225 |
0.444 |
| SMC |
5 |
7.433 |
3.4e-08 |
55.326 |
| SMC |
10 |
6.763 |
2.01e-07 |
76.018 |
| SMC |
15 |
12.982 |
9.16e-14 |
22.368 |
| SMC |
30 |
33.659 |
6.52e-25 |
105.705 |
| Metro |
2 |
1.905 |
0.0631 |
0.725 |
| Metro |
5 |
2.961 |
0.00575 |
2.474 |
| Metro |
10 |
5.879 |
1.63e-06 |
5.248 |
| Metro |
15 |
2.299 |
0.0286 |
2.829 |
| Metro |
30 |
6.695 |
2.22e-07 |
13.216 |
| DEMetro_Z |
2 |
3.653 |
0.000765 |
1.736 |
| DEMetro_Z |
5 |
2.941 |
0.00636 |
59.803 |
| DEMetro_Z |
10 |
9.153 |
4.72e-10 |
187.133 |
| DEMetro_Z |
15 |
13.969 |
1.99e-14 |
72.707 |
| DEMetro_Z |
30 |
21.464 |
2.39e-19 |
495.568 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-3.590
|
0.0012
|
-0.656
|
| HMC_vs_DEMetro_Z |
1
|
-2.916
|
0.00678
|
-0.532
|
| HMC_vs_DEMetro_Z |
2
|
-8.956
|
7.57e-10
|
-1.635
|
| HMC_vs_DEMetro_Z |
3
|
-10.261
|
3.67e-11
|
-1.873
|
| HMC_vs_DEMetro_Z |
4
|
-20.791
|
5.73e-19
|
-3.796
|
| Metro_vs_SMC |
0
|
0.648
|
0.522
|
0.118
|
| Metro_vs_SMC |
1
|
-7.120
|
7.79e-08
|
-1.300
|
| Metro_vs_SMC |
2
|
-6.258
|
7.87e-07
|
-1.143
|
| Metro_vs_SMC |
3
|
-8.588
|
1.85e-09
|
-1.568
|
| Metro_vs_SMC |
4
|
-26.866
|
4.84e-22
|
-4.905
|
| Metro_vs_DEMetro_Z |
0
|
-1.675
|
0.105
|
-0.306
|
| Metro_vs_DEMetro_Z |
1
|
-2.821
|
0.00855
|
-0.515
|
| Metro_vs_DEMetro_Z |
2
|
-8.803
|
1.1e-09
|
-1.607
|
| Metro_vs_DEMetro_Z |
3
|
-12.837
|
1.73e-13
|
-2.344
|
| Metro_vs_DEMetro_Z |
4
|
-21.324
|
2.87e-19
|
-3.893
|
| HMC_vs_Metro |
0
|
-1.564
|
0.129
|
-0.286
|
| HMC_vs_Metro |
1
|
-2.295
|
0.0292
|
-0.419
|
| HMC_vs_Metro |
2
|
-0.923
|
0.364
|
-0.169
|
| HMC_vs_Metro |
3
|
0.531
|
0.599
|
0.097
|
| HMC_vs_Metro |
4
|
-3.911
|
0.000509
|
-0.714
|
| HMC_vs_SMC |
0
|
-0.997
|
0.327
|
-0.182
|
| HMC_vs_SMC |
1
|
-7.372
|
4.03e-08
|
-1.346
|
| HMC_vs_SMC |
2
|
-6.328
|
6.51e-07
|
-1.155
|
| HMC_vs_SMC |
3
|
-3.281
|
0.0027
|
-0.599
|
| HMC_vs_SMC |
4
|
-27.450
|
2.65e-22
|
-5.012
|
| DEMetro_Z_vs_SMC |
0
|
2.472
|
0.0196
|
0.451
|
| DEMetro_Z_vs_SMC |
1
|
0.208
|
0.837
|
0.038
|
| DEMetro_Z_vs_SMC |
2
|
5.758
|
3.1e-06
|
1.051
|
| DEMetro_Z_vs_SMC |
3
|
9.982
|
6.88e-11
|
1.822
|
| DEMetro_Z_vs_SMC |
4
|
16.840
|
1.64e-16
|
3.075
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.068 |
0.065 |
0.042 |
0.085 |
| HMC |
5 |
0.069 |
0.064 |
0.020 |
0.294 |
| HMC |
10 |
0.104 |
0.061 |
0.015 |
2.880 |
| HMC |
15 |
0.370 |
0.073 |
0.054 |
5.500 |
| HMC |
30 |
0.111 |
0.064 |
0.016 |
2.994 |
| SMC |
2 |
0.083 |
0.065 |
0.042 |
0.444 |
| SMC |
5 |
1.181 |
0.064 |
0.020 |
55.326 |
| SMC |
10 |
1.188 |
0.061 |
0.015 |
76.018 |
| SMC |
15 |
1.279 |
0.073 |
0.054 |
22.368 |
| SMC |
30 |
1.734 |
0.064 |
0.016 |
105.705 |
| Metro |
2 |
0.095 |
0.065 |
0.042 |
0.725 |
| Metro |
5 |
0.113 |
0.064 |
0.020 |
2.474 |
| Metro |
10 |
0.139 |
0.061 |
0.015 |
5.248 |
| Metro |
15 |
0.226 |
0.073 |
0.054 |
2.829 |
| Metro |
30 |
0.273 |
0.064 |
0.016 |
13.216 |
| DEMetro_Z |
2 |
0.138 |
0.065 |
0.042 |
1.736 |
| DEMetro_Z |
5 |
1.271 |
0.064 |
0.020 |
59.803 |
| DEMetro_Z |
10 |
2.836 |
0.061 |
0.015 |
187.133 |
| DEMetro_Z |
15 |
3.993 |
0.073 |
0.054 |
72.707 |
| DEMetro_Z |
30 |
7.895 |
0.064 |
0.016 |
495.568 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
-1.831 |
0.0757 |
-0.351 |
| HMC |
5 |
-2.040 |
0.0473 |
-0.424 |
| HMC |
10 |
-0.078 |
0.938 |
-0.019 |
| HMC |
15 |
-0.635 |
0.53 |
-0.123 |
| HMC |
30 |
2.227 |
0.0328 |
1.499 |
| SMC |
2 |
-0.422 |
0.676 |
-0.081 |
| SMC |
5 |
13.844 |
2.47e-14 |
63.119 |
| SMC |
10 |
27.610 |
2.2e-22 |
265.437 |
| SMC |
15 |
55.738 |
1.28e-51 |
15.254 |
| SMC |
30 |
88.508 |
7.17e-37 |
696.555 |
| Metro |
2 |
-1.738 |
0.0913 |
-0.330 |
| Metro |
5 |
-0.967 |
0.338 |
-0.217 |
| Metro |
10 |
1.017 |
0.313 |
0.241 |
| Metro |
15 |
-0.574 |
0.569 |
-0.114 |
| Metro |
30 |
3.238 |
0.00287 |
3.274 |
| DEMetro_Z |
2 |
-1.592 |
0.121 |
-0.304 |
| DEMetro_Z |
5 |
1.352 |
0.187 |
29.668 |
| DEMetro_Z |
10 |
4.109 |
0.000297 |
45.320 |
| DEMetro_Z |
15 |
4.760 |
2.14e-05 |
1.877 |
| DEMetro_Z |
30 |
9.055 |
5.95e-10 |
104.150 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
-3.475
|
0.00163
|
-0.635
|
| HMC_vs_SMC |
1
|
-13.994
|
1.98e-14
|
-2.555
|
| HMC_vs_SMC |
2
|
-27.587
|
2.31e-22
|
-5.037
|
| HMC_vs_SMC |
3
|
-71.631
|
3.46e-34
|
-13.078
|
| HMC_vs_SMC |
4
|
-87.946
|
9.26e-37
|
-16.057
|
| Metro_vs_DEMetro_Z |
0
|
-1.384
|
0.177
|
-0.253
|
| Metro_vs_DEMetro_Z |
1
|
-1.362
|
0.184
|
-0.249
|
| Metro_vs_DEMetro_Z |
2
|
-4.118
|
0.00029
|
-0.752
|
| Metro_vs_DEMetro_Z |
3
|
-5.597
|
4.84e-06
|
-1.022
|
| Metro_vs_DEMetro_Z |
4
|
-8.865
|
9.42e-10
|
-1.619
|
| HMC_vs_Metro |
0
|
-0.663
|
0.512
|
-0.121
|
| HMC_vs_Metro |
1
|
-2.098
|
0.0447
|
-0.383
|
| HMC_vs_Metro |
2
|
-1.621
|
0.116
|
-0.296
|
| HMC_vs_Metro |
3
|
-0.090
|
0.929
|
-0.017
|
| HMC_vs_Metro |
4
|
-1.434
|
0.162
|
-0.262
|
| HMC_vs_DEMetro_Z |
0
|
-1.644
|
0.111
|
-0.300
|
| HMC_vs_DEMetro_Z |
1
|
-1.372
|
0.181
|
-0.250
|
| HMC_vs_DEMetro_Z |
2
|
-4.115
|
0.000292
|
-0.751
|
| HMC_vs_DEMetro_Z |
3
|
-5.494
|
6.44e-06
|
-1.003
|
| HMC_vs_DEMetro_Z |
4
|
-8.824
|
1.04e-09
|
-1.611
|
| Metro_vs_SMC |
0
|
-3.238
|
0.00301
|
-0.591
|
| Metro_vs_SMC |
1
|
-14.071
|
1.73e-14
|
-2.569
|
| Metro_vs_SMC |
2
|
-27.582
|
2.32e-22
|
-5.036
|
| Metro_vs_SMC |
3
|
-67.788
|
1.7e-33
|
-12.376
|
| Metro_vs_SMC |
4
|
-89.288
|
5.98e-37
|
-16.302
|
| DEMetro_Z_vs_SMC |
0
|
-2.951
|
0.00621
|
-0.539
|
| DEMetro_Z_vs_SMC |
1
|
-1.481
|
0.149
|
-0.270
|
| DEMetro_Z_vs_SMC |
2
|
-14.867
|
4.22e-15
|
-2.714
|
| DEMetro_Z_vs_SMC |
3
|
-32.142
|
3.15e-24
|
-5.868
|
| DEMetro_Z_vs_SMC |
4
|
-41.667
|
1.98e-27
|
-7.607
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
4.113 |
9.112 |
14.240 |
-0.351 |
| HMC |
5 |
4.972 |
8.258 |
7.752 |
-0.424 |
| HMC |
10 |
5.776 |
5.887 |
5.869 |
-0.019 |
| HMC |
15 |
15.662 |
33.673 |
146.019 |
-0.123 |
| HMC |
30 |
11.456 |
5.303 |
4.104 |
1.499 |
| SMC |
2 |
7.953 |
9.112 |
14.240 |
-0.081 |
| SMC |
5 |
497.557 |
8.258 |
7.752 |
63.119 |
| SMC |
10 |
1563.684 |
5.887 |
5.869 |
265.437 |
| SMC |
15 |
2260.978 |
33.673 |
146.019 |
15.254 |
| SMC |
30 |
2864.137 |
5.303 |
4.104 |
696.555 |
| Metro |
2 |
4.407 |
9.112 |
14.240 |
-0.330 |
| Metro |
5 |
6.573 |
8.258 |
7.752 |
-0.217 |
| Metro |
10 |
7.302 |
5.887 |
5.869 |
0.241 |
| Metro |
15 |
17.043 |
33.673 |
146.019 |
-0.114 |
| Metro |
30 |
18.741 |
5.303 |
4.104 |
3.274 |
| DEMetro_Z |
2 |
4.787 |
9.112 |
14.240 |
-0.304 |
| DEMetro_Z |
5 |
238.239 |
8.258 |
7.752 |
29.668 |
| DEMetro_Z |
10 |
271.860 |
5.887 |
5.869 |
45.320 |
| DEMetro_Z |
15 |
307.782 |
33.673 |
146.019 |
1.877 |
| DEMetro_Z |
30 |
432.759 |
5.303 |
4.104 |
104.150 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
1.885 |
0.067 |
0.889 |
| HMC |
5 |
2.387 |
0.0227 |
1.531 |
| HMC |
10 |
2.188 |
0.0368 |
6.846 |
| HMC |
15 |
1.638 |
0.112 |
9.730 |
| HMC |
30 |
2.887 |
0.00726 |
22.632 |
| SMC |
2 |
8.326 |
2.73e-09 |
11.831 |
| SMC |
5 |
23.847 |
1.32e-20 |
604.960 |
| SMC |
10 |
45.857 |
1.28e-28 |
1707.268 |
| SMC |
15 |
139.774 |
1.12e-42 |
695.164 |
| SMC |
30 |
168.272 |
6.28e-45 |
2302.342 |
| Metro |
2 |
6.480 |
4.11e-08 |
2.194 |
| Metro |
5 |
7.318 |
2.13e-08 |
5.267 |
| Metro |
10 |
5.212 |
1.37e-05 |
14.245 |
| Metro |
15 |
3.331 |
0.00235 |
8.222 |
| Metro |
30 |
4.235 |
0.00021 |
53.019 |
| DEMetro_Z |
2 |
8.369 |
2.04e-10 |
3.610 |
| DEMetro_Z |
5 |
3.393 |
0.00201 |
117.458 |
| DEMetro_Z |
10 |
7.216 |
6.05e-08 |
478.186 |
| DEMetro_Z |
15 |
11.598 |
2.06e-12 |
206.654 |
| DEMetro_Z |
30 |
17.336 |
7.6e-17 |
817.201 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-3.057
|
0.00477
|
-0.558
|
| Metro_vs_DEMetro_Z |
1
|
-3.237
|
0.00302
|
-0.591
|
| Metro_vs_DEMetro_Z |
2
|
-7.083
|
8.6e-08
|
-1.293
|
| Metro_vs_DEMetro_Z |
3
|
-10.971
|
7.74e-12
|
-2.003
|
| Metro_vs_DEMetro_Z |
4
|
-16.575
|
2.49e-16
|
-3.026
|
| DEMetro_Z_vs_SMC |
0
|
-5.854
|
2.38e-06
|
-1.069
|
| DEMetro_Z_vs_SMC |
1
|
-11.489
|
2.59e-12
|
-2.098
|
| DEMetro_Z_vs_SMC |
2
|
-15.623
|
1.17e-15
|
-2.852
|
| DEMetro_Z_vs_SMC |
3
|
-25.565
|
1.93e-21
|
-4.667
|
| DEMetro_Z_vs_SMC |
4
|
-30.003
|
2.19e-23
|
-5.478
|
| HMC_vs_DEMetro_Z |
0
|
-5.513
|
6.1e-06
|
-1.007
|
| HMC_vs_DEMetro_Z |
1
|
-3.342
|
0.0023
|
-0.610
|
| HMC_vs_DEMetro_Z |
2
|
-7.119
|
7.81e-08
|
-1.300
|
| HMC_vs_DEMetro_Z |
3
|
-10.527
|
2.03e-11
|
-1.922
|
| HMC_vs_DEMetro_Z |
4
|
-15.700
|
1.03e-15
|
-2.866
|
| HMC_vs_Metro |
0
|
-2.499
|
0.0184
|
-0.456
|
| HMC_vs_Metro |
1
|
-3.749
|
0.000787
|
-0.684
|
| HMC_vs_Metro |
2
|
-1.653
|
0.109
|
-0.302
|
| HMC_vs_Metro |
3
|
0.226
|
0.823
|
0.041
|
| HMC_vs_Metro |
4
|
-1.925
|
0.0641
|
-0.351
|
| HMC_vs_SMC |
0
|
-7.978
|
8.47e-09
|
-1.457
|
| HMC_vs_SMC |
1
|
-23.701
|
1.57e-20
|
-4.327
|
| HMC_vs_SMC |
2
|
-45.538
|
1.56e-28
|
-8.314
|
| HMC_vs_SMC |
3
|
-85.711
|
1.95e-36
|
-15.649
|
| HMC_vs_SMC |
4
|
-148.053
|
2.64e-43
|
-27.031
|
| Metro_vs_SMC |
0
|
-6.659
|
2.66e-07
|
-1.216
|
| Metro_vs_SMC |
1
|
-23.907
|
1.24e-20
|
-4.365
|
| Metro_vs_SMC |
2
|
-45.436
|
1.67e-28
|
-8.295
|
| Metro_vs_SMC |
3
|
-119.356
|
1.35e-40
|
-21.791
|
| Metro_vs_SMC |
4
|
-131.482
|
8.21e-42
|
-24.005
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.155 |
0.124 |
0.035 |
0.889 |
| HMC |
5 |
0.157 |
0.122 |
0.023 |
1.531 |
| HMC |
10 |
0.233 |
0.117 |
0.017 |
6.846 |
| HMC |
15 |
0.633 |
0.131 |
0.052 |
9.730 |
| HMC |
30 |
0.520 |
0.117 |
0.018 |
22.632 |
| SMC |
2 |
0.537 |
0.124 |
0.035 |
11.831 |
| SMC |
5 |
13.970 |
0.122 |
0.023 |
604.960 |
| SMC |
10 |
28.989 |
0.117 |
0.017 |
1707.268 |
| SMC |
15 |
35.983 |
0.131 |
0.052 |
695.164 |
| SMC |
30 |
41.099 |
0.117 |
0.018 |
2302.342 |
| Metro |
2 |
0.201 |
0.124 |
0.035 |
2.194 |
| Metro |
5 |
0.243 |
0.122 |
0.023 |
5.267 |
| Metro |
10 |
0.358 |
0.117 |
0.017 |
14.245 |
| Metro |
15 |
0.555 |
0.131 |
0.052 |
8.222 |
| Metro |
30 |
1.061 |
0.117 |
0.018 |
53.019 |
| DEMetro_Z |
2 |
0.250 |
0.124 |
0.035 |
3.610 |
| DEMetro_Z |
5 |
2.811 |
0.122 |
0.023 |
117.458 |
| DEMetro_Z |
10 |
8.204 |
0.117 |
0.017 |
478.186 |
| DEMetro_Z |
15 |
10.789 |
0.131 |
0.052 |
206.654 |
| DEMetro_Z |
30 |
14.664 |
0.117 |
0.018 |
817.201 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
2.744 |
0.00835 |
0.891 |
| HMC |
5 |
1.782 |
0.0851 |
3.294 |
| HMC |
10 |
1.640 |
0.112 |
15.634 |
| HMC |
15 |
2.359 |
0.0253 |
32.959 |
| HMC |
30 |
3.191 |
0.0034 |
33.083 |
| SMC |
2 |
10.338 |
2.55e-11 |
20.641 |
| SMC |
5 |
90.327 |
1.21e-37 |
171.338 |
| SMC |
10 |
120.876 |
1.33e-41 |
196.155 |
| SMC |
15 |
166.860 |
1.88e-46 |
206.681 |
| SMC |
30 |
202.869 |
1.42e-50 |
184.386 |
| Metro |
2 |
8.019 |
7.36e-10 |
3.600 |
| Metro |
5 |
8.100 |
4.01e-09 |
8.572 |
| Metro |
10 |
5.926 |
1.91e-06 |
21.169 |
| Metro |
15 |
7.140 |
7.29e-08 |
38.412 |
| Metro |
30 |
6.659 |
2.64e-07 |
57.060 |
| DEMetro_Z |
2 |
9.289 |
2.65e-11 |
4.615 |
| DEMetro_Z |
5 |
7.949 |
9.06e-09 |
77.180 |
| DEMetro_Z |
10 |
20.890 |
4.94e-19 |
207.076 |
| DEMetro_Z |
15 |
34.008 |
6.07e-25 |
247.217 |
| DEMetro_Z |
30 |
51.895 |
3.18e-30 |
247.955 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
-8.018
|
7.66e-09
|
-1.464
|
| DEMetro_Z_vs_SMC |
1
|
-9.513
|
2.02e-10
|
-1.737
|
| DEMetro_Z_vs_SMC |
2
|
1.162
|
0.255
|
0.212
|
| DEMetro_Z_vs_SMC |
3
|
5.594
|
4.87e-06
|
1.021
|
| DEMetro_Z_vs_SMC |
4
|
13.677
|
3.54e-14
|
2.497
|
| HMC_vs_Metro |
0
|
-5.333
|
1.01e-05
|
-0.974
|
| HMC_vs_Metro |
1
|
-2.265
|
0.0312
|
-0.414
|
| HMC_vs_Metro |
2
|
-0.523
|
0.605
|
-0.095
|
| HMC_vs_Metro |
3
|
-0.339
|
0.737
|
-0.062
|
| HMC_vs_Metro |
4
|
-1.619
|
0.116
|
-0.296
|
| Metro_vs_DEMetro_Z |
0
|
-1.743
|
0.0919
|
-0.318
|
| Metro_vs_DEMetro_Z |
1
|
-7.062
|
9.08e-08
|
-1.289
|
| Metro_vs_DEMetro_Z |
2
|
-16.701
|
2.04e-16
|
-3.049
|
| Metro_vs_DEMetro_Z |
3
|
-25.465
|
2.15e-21
|
-4.649
|
| Metro_vs_DEMetro_Z |
4
|
-19.413
|
3.68e-18
|
-3.544
|
| HMC_vs_SMC |
0
|
-9.970
|
7.06e-11
|
-1.820
|
| HMC_vs_SMC |
1
|
-56.504
|
3.21e-31
|
-10.316
|
| HMC_vs_SMC |
2
|
-18.502
|
1.34e-17
|
-3.378
|
| HMC_vs_SMC |
3
|
-12.640
|
2.54e-13
|
-2.308
|
| HMC_vs_SMC |
4
|
-14.916
|
3.88e-15
|
-2.723
|
| Metro_vs_SMC |
0
|
-8.188
|
4.99e-09
|
-1.495
|
| Metro_vs_SMC |
1
|
-76.431
|
5.33e-35
|
-13.954
|
| Metro_vs_SMC |
2
|
-45.162
|
1.98e-28
|
-8.245
|
| Metro_vs_SMC |
3
|
-31.369
|
6.26e-24
|
-5.727
|
| Metro_vs_SMC |
4
|
-14.725
|
5.41e-15
|
-2.688
|
| HMC_vs_DEMetro_Z |
0
|
-6.969
|
1.16e-07
|
-1.272
|
| HMC_vs_DEMetro_Z |
1
|
-7.144
|
7.31e-08
|
-1.304
|
| HMC_vs_DEMetro_Z |
2
|
-13.865
|
2.51e-14
|
-2.531
|
| HMC_vs_DEMetro_Z |
3
|
-14.830
|
4.51e-15
|
-2.708
|
| HMC_vs_DEMetro_Z |
4
|
-22.448
|
7.03e-20
|
-4.098
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.019 |
0.015 |
0.005 |
0.891 |
| HMC |
5 |
0.024 |
0.015 |
0.003 |
3.294 |
| HMC |
10 |
0.051 |
0.015 |
0.002 |
15.634 |
| HMC |
15 |
0.083 |
0.015 |
0.002 |
32.959 |
| HMC |
30 |
0.087 |
0.016 |
0.002 |
33.083 |
| SMC |
2 |
0.108 |
0.015 |
0.005 |
20.641 |
| SMC |
5 |
0.507 |
0.015 |
0.003 |
171.338 |
| SMC |
10 |
0.467 |
0.015 |
0.002 |
196.155 |
| SMC |
15 |
0.443 |
0.015 |
0.002 |
206.681 |
| SMC |
30 |
0.413 |
0.016 |
0.002 |
184.386 |
| Metro |
2 |
0.031 |
0.015 |
0.005 |
3.600 |
| Metro |
5 |
0.039 |
0.015 |
0.003 |
8.572 |
| Metro |
10 |
0.064 |
0.015 |
0.002 |
21.169 |
| Metro |
15 |
0.095 |
0.015 |
0.002 |
38.412 |
| Metro |
30 |
0.138 |
0.016 |
0.002 |
57.060 |
| DEMetro_Z |
2 |
0.036 |
0.015 |
0.005 |
4.615 |
| DEMetro_Z |
5 |
0.236 |
0.015 |
0.003 |
77.180 |
| DEMetro_Z |
10 |
0.493 |
0.015 |
0.002 |
207.076 |
| DEMetro_Z |
15 |
0.526 |
0.015 |
0.002 |
247.217 |
| DEMetro_Z |
30 |
0.550 |
0.016 |
0.002 |
247.955 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
KDE + Init Plots
Trace Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Vary_Dimension_with_high_Multimodality
(Mixture,
dimension,
30 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
5.873 |
2.23e-06 |
23.747 |
| HMC |
5 |
7.342 |
4.21e-08 |
26.116 |
| HMC |
10 |
5.451 |
7.2e-06 |
28.380 |
| HMC |
15 |
5.482 |
6.58e-06 |
25.682 |
| HMC |
30 |
5.050 |
2.21e-05 |
50.088 |
| SMC |
2 |
0.595 |
0.554 |
0.163 |
| SMC |
5 |
-1.084 |
0.283 |
-0.255 |
| SMC |
10 |
-0.011 |
0.991 |
-0.003 |
| SMC |
15 |
0.349 |
0.728 |
0.086 |
| SMC |
30 |
1.080 |
0.286 |
0.396 |
| Metro |
2 |
6.913 |
1.32e-07 |
26.937 |
| Metro |
5 |
6.172 |
9.79e-07 |
26.555 |
| Metro |
10 |
6.337 |
6.26e-07 |
29.903 |
| Metro |
15 |
6.462 |
4.46e-07 |
31.635 |
| Metro |
30 |
5.321 |
1.04e-05 |
53.862 |
| DEMetro_Z |
2 |
5.997 |
1.56e-06 |
19.081 |
| DEMetro_Z |
5 |
11.694 |
1.64e-12 |
64.051 |
| DEMetro_Z |
10 |
22.919 |
3.91e-20 |
257.289 |
| DEMetro_Z |
15 |
22.361 |
7.74e-20 |
324.790 |
| DEMetro_Z |
30 |
33.417 |
1.04e-24 |
959.339 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
0.984
|
0.333
|
0.180
|
| HMC_vs_DEMetro_Z |
1
|
-5.545
|
5.59e-06
|
-1.012
|
| HMC_vs_DEMetro_Z |
2
|
-19.389
|
3.8e-18
|
-3.540
|
| HMC_vs_DEMetro_Z |
3
|
-19.954
|
1.75e-18
|
-3.643
|
| HMC_vs_DEMetro_Z |
4
|
-34.022
|
6.31e-25
|
-6.211
|
| Metro_vs_SMC |
0
|
6.832
|
1.67e-07
|
1.247
|
| Metro_vs_SMC |
1
|
6.255
|
7.93e-07
|
1.142
|
| Metro_vs_SMC |
2
|
6.299
|
7.03e-07
|
1.150
|
| Metro_vs_SMC |
3
|
6.465
|
4.49e-07
|
1.180
|
| Metro_vs_SMC |
4
|
5.296
|
1.11e-05
|
0.967
|
| Metro_vs_DEMetro_Z |
0
|
1.685
|
0.103
|
0.308
|
| Metro_vs_DEMetro_Z |
1
|
-5.346
|
9.7e-06
|
-0.976
|
| Metro_vs_DEMetro_Z |
2
|
-18.887
|
7.7e-18
|
-3.448
|
| Metro_vs_DEMetro_Z |
3
|
-19.721
|
2.4e-18
|
-3.600
|
| Metro_vs_DEMetro_Z |
4
|
-33.261
|
1.2e-24
|
-6.073
|
| HMC_vs_Metro |
0
|
-1.004
|
0.324
|
-0.183
|
| HMC_vs_Metro |
1
|
-0.136
|
0.893
|
-0.025
|
| HMC_vs_Metro |
2
|
-0.243
|
0.81
|
-0.044
|
| HMC_vs_Metro |
3
|
-0.890
|
0.381
|
-0.163
|
| HMC_vs_Metro |
4
|
-0.700
|
0.489
|
-0.128
|
| HMC_vs_SMC |
0
|
5.782
|
2.9e-06
|
1.056
|
| HMC_vs_SMC |
1
|
7.517
|
2.76e-08
|
1.372
|
| HMC_vs_SMC |
2
|
5.520
|
5.99e-06
|
1.008
|
| HMC_vs_SMC |
3
|
5.440
|
7.47e-06
|
0.993
|
| HMC_vs_SMC |
4
|
5.011
|
2.46e-05
|
0.915
|
| DEMetro_Z_vs_SMC |
0
|
5.932
|
1.92e-06
|
1.083
|
| DEMetro_Z_vs_SMC |
1
|
11.763
|
1.47e-12
|
2.148
|
| DEMetro_Z_vs_SMC |
2
|
23.004
|
3.58e-20
|
4.200
|
| DEMetro_Z_vs_SMC |
3
|
22.331
|
8.1e-20
|
4.077
|
| DEMetro_Z_vs_SMC |
4
|
33.376
|
1.09e-24
|
6.094
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
1.426 |
0.081 |
0.057 |
23.747 |
| HMC |
5 |
1.174 |
0.062 |
0.043 |
26.116 |
| HMC |
10 |
0.606 |
0.045 |
0.020 |
28.380 |
| HMC |
15 |
0.511 |
0.040 |
0.018 |
25.682 |
| HMC |
30 |
0.376 |
0.029 |
0.007 |
50.088 |
| SMC |
2 |
0.090 |
0.081 |
0.057 |
0.163 |
| SMC |
5 |
0.051 |
0.062 |
0.043 |
-0.255 |
| SMC |
10 |
0.045 |
0.045 |
0.020 |
-0.003 |
| SMC |
15 |
0.042 |
0.040 |
0.018 |
0.086 |
| SMC |
30 |
0.032 |
0.029 |
0.007 |
0.396 |
| Metro |
2 |
1.607 |
0.081 |
0.057 |
26.937 |
| Metro |
5 |
1.193 |
0.062 |
0.043 |
26.555 |
| Metro |
10 |
0.637 |
0.045 |
0.020 |
29.903 |
| Metro |
15 |
0.621 |
0.040 |
0.018 |
31.635 |
| Metro |
30 |
0.403 |
0.029 |
0.007 |
53.862 |
| DEMetro_Z |
2 |
1.162 |
0.081 |
0.057 |
19.081 |
| DEMetro_Z |
5 |
2.789 |
0.062 |
0.043 |
64.051 |
| DEMetro_Z |
10 |
5.137 |
0.045 |
0.020 |
257.289 |
| DEMetro_Z |
15 |
6.000 |
0.040 |
0.018 |
324.790 |
| DEMetro_Z |
30 |
6.683 |
0.029 |
0.007 |
959.339 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
4.375 |
0.000143 |
45.694 |
| HMC |
5 |
5.022 |
2.38e-05 |
61.701 |
| HMC |
10 |
4.160 |
0.000258 |
48.951 |
| HMC |
15 |
4.117 |
0.000291 |
51.350 |
| HMC |
30 |
3.903 |
0.00052 |
67.473 |
| SMC |
2 |
0.976 |
0.333 |
0.270 |
| SMC |
5 |
-0.635 |
0.528 |
-0.174 |
| SMC |
10 |
0.734 |
0.466 |
0.193 |
| SMC |
15 |
0.345 |
0.731 |
0.110 |
| SMC |
30 |
2.208 |
0.0321 |
0.784 |
| Metro |
2 |
4.837 |
3.98e-05 |
51.229 |
| Metro |
5 |
4.747 |
5.11e-05 |
72.973 |
| Metro |
10 |
4.764 |
4.88e-05 |
46.801 |
| Metro |
15 |
4.582 |
8.08e-05 |
68.283 |
| Metro |
30 |
4.002 |
0.000398 |
73.572 |
| DEMetro_Z |
2 |
3.439 |
0.00179 |
28.988 |
| DEMetro_Z |
5 |
6.972 |
1.15e-07 |
528.854 |
| DEMetro_Z |
10 |
19.614 |
2.78e-18 |
2637.129 |
| DEMetro_Z |
15 |
25.150 |
3.04e-21 |
4219.731 |
| DEMetro_Z |
30 |
33.455 |
1.01e-24 |
7619.194 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
4.372
|
0.000144
|
0.798
|
| HMC_vs_SMC |
1
|
5.021
|
2.39e-05
|
0.917
|
| HMC_vs_SMC |
2
|
4.159
|
0.000259
|
0.759
|
| HMC_vs_SMC |
3
|
4.109
|
0.000297
|
0.750
|
| HMC_vs_SMC |
4
|
3.852
|
0.000597
|
0.703
|
| Metro_vs_DEMetro_Z |
0
|
1.707
|
0.0985
|
0.312
|
| Metro_vs_DEMetro_Z |
1
|
-5.743
|
3.23e-06
|
-1.048
|
| Metro_vs_DEMetro_Z |
2
|
-18.925
|
7.3e-18
|
-3.455
|
| Metro_vs_DEMetro_Z |
3
|
-24.640
|
5.37e-21
|
-4.499
|
| Metro_vs_DEMetro_Z |
4
|
-32.369
|
2.58e-24
|
-5.910
|
| HMC_vs_Metro |
0
|
-0.992
|
0.329
|
-0.181
|
| HMC_vs_Metro |
1
|
-0.776
|
0.444
|
-0.142
|
| HMC_vs_Metro |
2
|
0.146
|
0.885
|
0.027
|
| HMC_vs_Metro |
3
|
-0.847
|
0.404
|
-0.155
|
| HMC_vs_Metro |
4
|
-0.644
|
0.524
|
-0.118
|
| HMC_vs_DEMetro_Z |
0
|
1.311
|
0.2
|
0.239
|
| HMC_vs_DEMetro_Z |
1
|
-5.970
|
1.73e-06
|
-1.090
|
| HMC_vs_DEMetro_Z |
2
|
-19.091
|
5.77e-18
|
-3.486
|
| HMC_vs_DEMetro_Z |
3
|
-24.631
|
5.42e-21
|
-4.497
|
| HMC_vs_DEMetro_Z |
4
|
-32.986
|
1.51e-24
|
-6.022
|
| Metro_vs_SMC |
0
|
4.845
|
3.91e-05
|
0.885
|
| Metro_vs_SMC |
1
|
4.767
|
4.85e-05
|
0.870
|
| Metro_vs_SMC |
2
|
4.719
|
5.53e-05
|
0.862
|
| Metro_vs_SMC |
3
|
4.578
|
8.18e-05
|
0.836
|
| Metro_vs_SMC |
4
|
3.964
|
0.000441
|
0.724
|
| DEMetro_Z_vs_SMC |
0
|
3.415
|
0.0019
|
0.624
|
| DEMetro_Z_vs_SMC |
1
|
6.972
|
1.15e-07
|
1.273
|
| DEMetro_Z_vs_SMC |
2
|
19.620
|
2.76e-18
|
3.582
|
| DEMetro_Z_vs_SMC |
3
|
25.159
|
3.01e-21
|
4.593
|
| DEMetro_Z_vs_SMC |
4
|
33.457
|
1.01e-24
|
6.108
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
5.137 |
0.141 |
0.109 |
45.694 |
| HMC |
5 |
4.613 |
0.114 |
0.073 |
61.701 |
| HMC |
10 |
2.218 |
0.076 |
0.044 |
48.951 |
| HMC |
15 |
1.811 |
0.071 |
0.034 |
51.350 |
| HMC |
30 |
1.571 |
0.052 |
0.023 |
67.473 |
| SMC |
2 |
0.170 |
0.141 |
0.109 |
0.270 |
| SMC |
5 |
0.101 |
0.114 |
0.073 |
-0.174 |
| SMC |
10 |
0.085 |
0.076 |
0.044 |
0.193 |
| SMC |
15 |
0.075 |
0.071 |
0.034 |
0.110 |
| SMC |
30 |
0.069 |
0.052 |
0.023 |
0.784 |
| Metro |
2 |
5.742 |
0.141 |
0.109 |
51.229 |
| Metro |
5 |
5.435 |
0.114 |
0.073 |
72.973 |
| Metro |
10 |
2.124 |
0.076 |
0.044 |
46.801 |
| Metro |
15 |
2.384 |
0.071 |
0.034 |
68.283 |
| Metro |
30 |
1.709 |
0.052 |
0.023 |
73.572 |
| DEMetro_Z |
2 |
3.310 |
0.141 |
0.109 |
28.988 |
| DEMetro_Z |
5 |
38.676 |
0.114 |
0.073 |
528.854 |
| DEMetro_Z |
10 |
115.465 |
0.076 |
0.044 |
2637.129 |
| DEMetro_Z |
15 |
142.987 |
0.071 |
0.034 |
4219.731 |
| DEMetro_Z |
30 |
171.651 |
0.052 |
0.023 |
7619.194 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
5.895 |
2.1e-06 |
27.181 |
| HMC |
5 |
7.056 |
9.05e-08 |
31.139 |
| HMC |
10 |
5.468 |
6.88e-06 |
33.848 |
| HMC |
15 |
5.441 |
7.39e-06 |
29.205 |
| HMC |
30 |
5.057 |
2.16e-05 |
61.765 |
| SMC |
2 |
0.549 |
0.585 |
0.152 |
| SMC |
5 |
-0.777 |
0.441 |
-0.183 |
| SMC |
10 |
0.587 |
0.559 |
0.169 |
| SMC |
15 |
0.080 |
0.937 |
0.019 |
| SMC |
30 |
1.694 |
0.0971 |
0.650 |
| Metro |
2 |
6.741 |
2.1e-07 |
29.851 |
| Metro |
5 |
6.135 |
1.09e-06 |
30.330 |
| Metro |
10 |
6.356 |
5.97e-07 |
36.174 |
| Metro |
15 |
6.377 |
5.64e-07 |
35.574 |
| Metro |
30 |
5.282 |
1.16e-05 |
67.357 |
| DEMetro_Z |
2 |
5.776 |
2.9e-06 |
21.376 |
| DEMetro_Z |
5 |
12.230 |
5.64e-13 |
112.530 |
| DEMetro_Z |
10 |
36.216 |
1.06e-25 |
593.375 |
| DEMetro_Z |
15 |
37.248 |
4.79e-26 |
690.302 |
| DEMetro_Z |
30 |
58.097 |
1.44e-31 |
2292.236 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
1.628
|
0.114
|
0.297
|
| Metro_vs_DEMetro_Z |
1
|
-7.675
|
1.84e-08
|
-1.401
|
| Metro_vs_DEMetro_Z |
2
|
-30.637
|
1.22e-23
|
-5.593
|
| Metro_vs_DEMetro_Z |
3
|
-34.058
|
6.12e-25
|
-6.218
|
| Metro_vs_DEMetro_Z |
4
|
-53.092
|
1.92e-30
|
-9.693
|
| DEMetro_Z_vs_SMC |
0
|
5.718
|
3.46e-06
|
1.044
|
| DEMetro_Z_vs_SMC |
1
|
12.249
|
5.49e-13
|
2.236
|
| DEMetro_Z_vs_SMC |
2
|
36.383
|
9.41e-26
|
6.643
|
| DEMetro_Z_vs_SMC |
3
|
37.191
|
5.04e-26
|
6.790
|
| DEMetro_Z_vs_SMC |
4
|
58.160
|
1.4e-31
|
10.619
|
| HMC_vs_DEMetro_Z |
0
|
1.070
|
0.293
|
0.195
|
| HMC_vs_DEMetro_Z |
1
|
-7.555
|
2.5e-08
|
-1.379
|
| HMC_vs_DEMetro_Z |
2
|
-32.684
|
1.96e-24
|
-5.967
|
| HMC_vs_DEMetro_Z |
3
|
-34.780
|
3.38e-25
|
-6.350
|
| HMC_vs_DEMetro_Z |
4
|
-56.929
|
2.59e-31
|
-10.394
|
| HMC_vs_Metro |
0
|
-0.739
|
0.466
|
-0.135
|
| HMC_vs_Metro |
1
|
0.197
|
0.845
|
0.036
|
| HMC_vs_Metro |
2
|
-0.311
|
0.758
|
-0.057
|
| HMC_vs_Metro |
3
|
-0.841
|
0.407
|
-0.153
|
| HMC_vs_Metro |
4
|
-0.785
|
0.439
|
-0.143
|
| HMC_vs_SMC |
0
|
5.815
|
2.65e-06
|
1.062
|
| HMC_vs_SMC |
1
|
7.191
|
6.46e-08
|
1.313
|
| HMC_vs_SMC |
2
|
5.512
|
6.12e-06
|
1.006
|
| HMC_vs_SMC |
3
|
5.416
|
8e-06
|
0.989
|
| HMC_vs_SMC |
4
|
5.001
|
2.53e-05
|
0.913
|
| Metro_vs_SMC |
0
|
6.653
|
2.7e-07
|
1.215
|
| Metro_vs_SMC |
1
|
6.192
|
9.41e-07
|
1.131
|
| Metro_vs_SMC |
2
|
6.302
|
6.97e-07
|
1.151
|
| Metro_vs_SMC |
3
|
6.390
|
5.5e-07
|
1.167
|
| Metro_vs_SMC |
4
|
5.239
|
1.31e-05
|
0.956
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
1.320 |
0.090 |
0.045 |
27.181 |
| HMC |
5 |
1.030 |
0.066 |
0.031 |
31.139 |
| HMC |
10 |
0.490 |
0.050 |
0.013 |
33.848 |
| HMC |
15 |
0.422 |
0.047 |
0.013 |
29.205 |
| HMC |
30 |
0.308 |
0.037 |
0.004 |
61.765 |
| SMC |
2 |
0.097 |
0.090 |
0.045 |
0.152 |
| SMC |
5 |
0.061 |
0.066 |
0.031 |
-0.183 |
| SMC |
10 |
0.052 |
0.050 |
0.013 |
0.169 |
| SMC |
15 |
0.047 |
0.047 |
0.013 |
0.019 |
| SMC |
30 |
0.040 |
0.037 |
0.004 |
0.650 |
| Metro |
2 |
1.440 |
0.090 |
0.045 |
29.851 |
| Metro |
5 |
1.005 |
0.066 |
0.031 |
30.330 |
| Metro |
10 |
0.520 |
0.050 |
0.013 |
36.174 |
| Metro |
15 |
0.503 |
0.047 |
0.013 |
35.574 |
| Metro |
30 |
0.332 |
0.037 |
0.004 |
67.357 |
| DEMetro_Z |
2 |
1.057 |
0.090 |
0.045 |
21.376 |
| DEMetro_Z |
5 |
3.550 |
0.066 |
0.031 |
112.530 |
| DEMetro_Z |
10 |
7.760 |
0.050 |
0.013 |
593.375 |
| DEMetro_Z |
15 |
8.894 |
0.047 |
0.013 |
690.302 |
| DEMetro_Z |
30 |
10.087 |
0.037 |
0.004 |
2292.236 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
5.905 |
2.04e-06 |
28.145 |
| HMC |
5 |
7.498 |
2.82e-08 |
30.428 |
| HMC |
10 |
5.448 |
7.27e-06 |
33.214 |
| HMC |
15 |
5.517 |
6e-06 |
32.594 |
| HMC |
30 |
5.088 |
1.99e-05 |
62.016 |
| SMC |
2 |
1.103 |
0.275 |
0.304 |
| SMC |
5 |
-1.096 |
0.278 |
-0.255 |
| SMC |
10 |
0.294 |
0.77 |
0.080 |
| SMC |
15 |
0.300 |
0.765 |
0.076 |
| SMC |
30 |
1.787 |
0.081 |
0.712 |
| Metro |
2 |
7.194 |
6.29e-08 |
32.076 |
| Metro |
5 |
6.263 |
7.67e-07 |
30.938 |
| Metro |
10 |
6.385 |
5.51e-07 |
35.545 |
| Metro |
15 |
6.470 |
4.39e-07 |
40.020 |
| Metro |
30 |
5.267 |
1.21e-05 |
68.195 |
| DEMetro_Z |
2 |
6.181 |
9.51e-07 |
23.167 |
| DEMetro_Z |
5 |
22.203 |
6.3e-20 |
48.017 |
| DEMetro_Z |
10 |
61.524 |
8.48e-33 |
110.471 |
| DEMetro_Z |
15 |
72.073 |
5.34e-35 |
112.647 |
| DEMetro_Z |
30 |
80.723 |
6.89e-36 |
245.154 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
6.111
|
1.18e-06
|
1.116
|
| DEMetro_Z_vs_SMC |
1
|
22.546
|
6.23e-20
|
4.116
|
| DEMetro_Z_vs_SMC |
2
|
61.763
|
2.48e-32
|
11.276
|
| DEMetro_Z_vs_SMC |
3
|
72.060
|
2.92e-34
|
13.156
|
| DEMetro_Z_vs_SMC |
4
|
80.823
|
1.06e-35
|
14.756
|
| HMC_vs_Metro |
0
|
-1.018
|
0.317
|
-0.186
|
| HMC_vs_Metro |
1
|
-0.138
|
0.891
|
-0.025
|
| HMC_vs_Metro |
2
|
-0.318
|
0.753
|
-0.058
|
| HMC_vs_Metro |
3
|
-0.875
|
0.389
|
-0.160
|
| HMC_vs_Metro |
4
|
-0.878
|
0.387
|
-0.160
|
| Metro_vs_DEMetro_Z |
0
|
1.658
|
0.108
|
0.303
|
| Metro_vs_DEMetro_Z |
1
|
-3.230
|
0.00307
|
-0.590
|
| Metro_vs_DEMetro_Z |
2
|
-12.595
|
2.77e-13
|
-2.299
|
| Metro_vs_DEMetro_Z |
3
|
-11.285
|
3.97e-12
|
-2.060
|
| Metro_vs_DEMetro_Z |
4
|
-15.442
|
1.59e-15
|
-2.819
|
| HMC_vs_SMC |
0
|
5.801
|
2.75e-06
|
1.059
|
| HMC_vs_SMC |
1
|
7.647
|
1.97e-08
|
1.396
|
| HMC_vs_SMC |
2
|
5.490
|
6.51e-06
|
1.002
|
| HMC_vs_SMC |
3
|
5.483
|
6.63e-06
|
1.001
|
| HMC_vs_SMC |
4
|
5.025
|
2.36e-05
|
0.917
|
| Metro_vs_SMC |
0
|
7.104
|
8.14e-08
|
1.297
|
| Metro_vs_SMC |
1
|
6.339
|
6.31e-07
|
1.157
|
| Metro_vs_SMC |
2
|
6.328
|
6.5e-07
|
1.155
|
| Metro_vs_SMC |
3
|
6.478
|
4.33e-07
|
1.183
|
| Metro_vs_SMC |
4
|
5.218
|
1.38e-05
|
0.953
|
| HMC_vs_DEMetro_Z |
0
|
0.882
|
0.385
|
0.161
|
| HMC_vs_DEMetro_Z |
1
|
-3.777
|
0.00073
|
-0.690
|
| HMC_vs_DEMetro_Z |
2
|
-13.426
|
5.65e-14
|
-2.451
|
| HMC_vs_DEMetro_Z |
3
|
-13.070
|
1.11e-13
|
-2.386
|
| HMC_vs_DEMetro_Z |
4
|
-15.656
|
1.11e-15
|
-2.858
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.216 |
0.012 |
0.007 |
28.145 |
| HMC |
5 |
0.267 |
0.014 |
0.008 |
30.428 |
| HMC |
10 |
0.181 |
0.014 |
0.005 |
33.214 |
| HMC |
15 |
0.177 |
0.014 |
0.005 |
32.594 |
| HMC |
30 |
0.154 |
0.013 |
0.002 |
62.016 |
| SMC |
2 |
0.014 |
0.012 |
0.007 |
0.304 |
| SMC |
5 |
0.012 |
0.014 |
0.008 |
-0.255 |
| SMC |
10 |
0.014 |
0.014 |
0.005 |
0.080 |
| SMC |
15 |
0.015 |
0.014 |
0.005 |
0.076 |
| SMC |
30 |
0.015 |
0.013 |
0.002 |
0.712 |
| Metro |
2 |
0.245 |
0.012 |
0.007 |
32.076 |
| Metro |
5 |
0.271 |
0.014 |
0.008 |
30.938 |
| Metro |
10 |
0.193 |
0.014 |
0.005 |
35.545 |
| Metro |
15 |
0.214 |
0.014 |
0.005 |
40.020 |
| Metro |
30 |
0.168 |
0.013 |
0.002 |
68.195 |
| DEMetro_Z |
2 |
0.180 |
0.012 |
0.007 |
23.167 |
| DEMetro_Z |
5 |
0.413 |
0.014 |
0.008 |
48.017 |
| DEMetro_Z |
10 |
0.570 |
0.014 |
0.005 |
110.471 |
| DEMetro_Z |
15 |
0.575 |
0.014 |
0.005 |
112.647 |
| DEMetro_Z |
30 |
0.570 |
0.013 |
0.002 |
245.154 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
256.602 |
9.06e-88 |
73.419 |
| HMC |
5 |
237.665 |
2.19e-88 |
61.459 |
| HMC |
10 |
274.370 |
1.18e-79 |
93.868 |
| HMC |
15 |
230.589 |
6.71e-74 |
82.098 |
| HMC |
30 |
303.731 |
3.99e-65 |
154.016 |
| SMC |
2 |
0.383 |
0.703 |
0.103 |
| SMC |
5 |
-1.574 |
0.121 |
-0.374 |
| SMC |
10 |
-0.492 |
0.625 |
-0.139 |
| SMC |
15 |
-0.043 |
0.966 |
-0.011 |
| SMC |
30 |
0.204 |
0.839 |
0.059 |
| Metro |
2 |
37.272 |
2.14e-26 |
70.750 |
| Metro |
5 |
20.722 |
4.92e-19 |
56.376 |
| Metro |
10 |
21.708 |
1.56e-19 |
85.652 |
| Metro |
15 |
20.459 |
7.74e-19 |
73.883 |
| Metro |
30 |
24.601 |
5.27e-21 |
142.986 |
| DEMetro_Z |
2 |
17.177 |
8.78e-17 |
66.312 |
| DEMetro_Z |
5 |
24.001 |
8.57e-21 |
67.428 |
| DEMetro_Z |
10 |
15.321 |
1.94e-15 |
344.334 |
| DEMetro_Z |
15 |
16.626 |
2.29e-16 |
517.736 |
| DEMetro_Z |
30 |
22.885 |
4.13e-20 |
1580.627 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
1.867
|
0.072
|
0.341
|
| HMC_vs_DEMetro_Z |
1
|
-2.119
|
0.0428
|
-0.387
|
| HMC_vs_DEMetro_Z |
2
|
-11.149
|
5.3e-12
|
-2.035
|
| HMC_vs_DEMetro_Z |
3
|
-13.989
|
2e-14
|
-2.554
|
| HMC_vs_DEMetro_Z |
4
|
-20.678
|
6.64e-19
|
-3.775
|
| Metro_vs_SMC |
0
|
36.665
|
7.56e-26
|
6.694
|
| Metro_vs_SMC |
1
|
21.000
|
4.36e-19
|
3.834
|
| Metro_vs_SMC |
2
|
21.445
|
2.46e-19
|
3.915
|
| Metro_vs_SMC |
3
|
20.753
|
6.02e-19
|
3.789
|
| Metro_vs_SMC |
4
|
24.451
|
6.64e-21
|
4.464
|
| Metro_vs_DEMetro_Z |
0
|
1.006
|
0.323
|
0.184
|
| Metro_vs_DEMetro_Z |
1
|
-2.995
|
0.00557
|
-0.547
|
| Metro_vs_DEMetro_Z |
2
|
-11.555
|
2.25e-12
|
-2.110
|
| Metro_vs_DEMetro_Z |
3
|
-14.588
|
6.88e-15
|
-2.663
|
| Metro_vs_DEMetro_Z |
4
|
-20.882
|
5.08e-19
|
-3.813
|
| HMC_vs_Metro |
0
|
1.400
|
0.172
|
0.256
|
| HMC_vs_Metro |
1
|
1.865
|
0.0723
|
0.341
|
| HMC_vs_Metro |
2
|
2.108
|
0.0438
|
0.385
|
| HMC_vs_Metro |
3
|
2.254
|
0.0319
|
0.412
|
| HMC_vs_Metro |
4
|
1.924
|
0.0642
|
0.351
|
| HMC_vs_SMC |
0
|
293.488
|
6.45e-52
|
53.583
|
| HMC_vs_SMC |
1
|
251.236
|
5.84e-50
|
45.869
|
| HMC_vs_SMC |
2
|
292.154
|
7.36e-52
|
53.340
|
| HMC_vs_SMC |
3
|
233.975
|
4.6e-49
|
42.718
|
| HMC_vs_SMC |
4
|
308.528
|
1.51e-52
|
56.329
|
| DEMetro_Z_vs_SMC |
0
|
17.198
|
9.39e-17
|
3.140
|
| DEMetro_Z_vs_SMC |
1
|
24.054
|
1.05e-20
|
4.392
|
| DEMetro_Z_vs_SMC |
2
|
15.331
|
1.91e-15
|
2.799
|
| DEMetro_Z_vs_SMC |
3
|
16.619
|
2.32e-16
|
3.034
|
| DEMetro_Z_vs_SMC |
4
|
22.877
|
4.17e-20
|
4.177
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
4.241 |
0.081 |
0.057 |
73.419 |
| HMC |
5 |
2.679 |
0.062 |
0.043 |
61.459 |
| HMC |
10 |
1.903 |
0.045 |
0.020 |
93.868 |
| HMC |
15 |
1.547 |
0.040 |
0.018 |
82.098 |
| HMC |
30 |
1.097 |
0.029 |
0.007 |
154.016 |
| SMC |
2 |
0.087 |
0.081 |
0.057 |
0.103 |
| SMC |
5 |
0.046 |
0.062 |
0.043 |
-0.374 |
| SMC |
10 |
0.042 |
0.045 |
0.020 |
-0.139 |
| SMC |
15 |
0.040 |
0.040 |
0.018 |
-0.011 |
| SMC |
30 |
0.029 |
0.029 |
0.007 |
0.059 |
| Metro |
2 |
4.089 |
0.081 |
0.057 |
70.750 |
| Metro |
5 |
2.463 |
0.062 |
0.043 |
56.376 |
| Metro |
10 |
1.740 |
0.045 |
0.020 |
85.652 |
| Metro |
15 |
1.396 |
0.040 |
0.018 |
73.883 |
| Metro |
30 |
1.021 |
0.029 |
0.007 |
142.986 |
| DEMetro_Z |
2 |
3.838 |
0.081 |
0.057 |
66.312 |
| DEMetro_Z |
5 |
2.933 |
0.062 |
0.043 |
67.428 |
| DEMetro_Z |
10 |
6.860 |
0.045 |
0.020 |
344.334 |
| DEMetro_Z |
15 |
9.540 |
0.040 |
0.018 |
517.736 |
| DEMetro_Z |
30 |
10.992 |
0.029 |
0.007 |
1580.627 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
785.937 |
3.07e-113 |
231.262 |
| HMC |
5 |
766.048 |
2.24e-114 |
219.243 |
| HMC |
10 |
864.675 |
2.43e-114 |
258.731 |
| HMC |
15 |
882.601 |
1.8e-112 |
272.540 |
| HMC |
30 |
791.204 |
2.66e-97 |
289.649 |
| SMC |
2 |
0.883 |
0.381 |
0.233 |
| SMC |
5 |
-0.940 |
0.351 |
-0.219 |
| SMC |
10 |
0.579 |
0.565 |
0.145 |
| SMC |
15 |
-0.095 |
0.925 |
-0.024 |
| SMC |
30 |
0.912 |
0.366 |
0.316 |
| Metro |
2 |
28.631 |
7.83e-23 |
219.664 |
| Metro |
5 |
17.594 |
5.07e-17 |
195.339 |
| Metro |
10 |
16.431 |
3.11e-16 |
229.509 |
| Metro |
15 |
16.383 |
3.36e-16 |
236.741 |
| Metro |
30 |
18.172 |
2.15e-17 |
260.372 |
| DEMetro_Z |
2 |
16.320 |
3.71e-16 |
208.282 |
| DEMetro_Z |
5 |
14.678 |
5.85e-15 |
237.134 |
| DEMetro_Z |
10 |
10.720 |
1.33e-11 |
534.623 |
| DEMetro_Z |
15 |
10.969 |
7.77e-12 |
651.708 |
| DEMetro_Z |
30 |
14.187 |
1.4e-14 |
941.299 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
662.577
|
3.59e-62
|
120.969
|
| HMC_vs_SMC |
1
|
710.202
|
4.8e-63
|
129.665
|
| HMC_vs_SMC |
2
|
1056.297
|
4.81e-68
|
192.853
|
| HMC_vs_SMC |
3
|
949.916
|
1.04e-66
|
173.430
|
| HMC_vs_SMC |
4
|
882.731
|
8.76e-66
|
161.164
|
| Metro_vs_DEMetro_Z |
0
|
0.733
|
0.469
|
0.134
|
| Metro_vs_DEMetro_Z |
1
|
-1.976
|
0.0578
|
-0.361
|
| Metro_vs_DEMetro_Z |
2
|
-6.348
|
6.17e-07
|
-1.159
|
| Metro_vs_DEMetro_Z |
3
|
-6.403
|
5.31e-07
|
-1.169
|
| Metro_vs_DEMetro_Z |
4
|
-10.496
|
2.17e-11
|
-1.916
|
| HMC_vs_Metro |
0
|
1.519
|
0.14
|
0.277
|
| HMC_vs_Metro |
1
|
2.148
|
0.0402
|
0.392
|
| HMC_vs_Metro |
2
|
2.099
|
0.0446
|
0.383
|
| HMC_vs_Metro |
3
|
2.484
|
0.019
|
0.453
|
| HMC_vs_Metro |
4
|
2.038
|
0.0508
|
0.372
|
| HMC_vs_DEMetro_Z |
0
|
1.791
|
0.0837
|
0.327
|
| HMC_vs_DEMetro_Z |
1
|
-1.107
|
0.277
|
-0.202
|
| HMC_vs_DEMetro_Z |
2
|
-5.525
|
5.9e-06
|
-1.009
|
| HMC_vs_DEMetro_Z |
3
|
-6.381
|
5.63e-07
|
-1.165
|
| HMC_vs_DEMetro_Z |
4
|
-9.831
|
9.7e-11
|
-1.795
|
| Metro_vs_SMC |
0
|
28.412
|
1.01e-22
|
5.187
|
| Metro_vs_SMC |
1
|
17.688
|
4.45e-17
|
3.229
|
| Metro_vs_SMC |
2
|
16.442
|
3.08e-16
|
3.002
|
| Metro_vs_SMC |
3
|
16.382
|
3.39e-16
|
2.991
|
| Metro_vs_SMC |
4
|
18.083
|
2.47e-17
|
3.301
|
| DEMetro_Z_vs_SMC |
0
|
16.323
|
3.72e-16
|
2.980
|
| DEMetro_Z_vs_SMC |
1
|
14.669
|
5.96e-15
|
2.678
|
| DEMetro_Z_vs_SMC |
2
|
10.711
|
1.36e-11
|
1.956
|
| DEMetro_Z_vs_SMC |
3
|
10.972
|
7.73e-12
|
2.003
|
| DEMetro_Z_vs_SMC |
4
|
14.188
|
1.4e-14
|
2.590
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
25.429 |
0.141 |
0.109 |
231.262 |
| HMC |
5 |
16.100 |
0.114 |
0.073 |
219.243 |
| HMC |
10 |
11.397 |
0.076 |
0.044 |
258.731 |
| HMC |
15 |
9.302 |
0.071 |
0.034 |
272.540 |
| HMC |
30 |
6.575 |
0.052 |
0.023 |
289.649 |
| SMC |
2 |
0.166 |
0.141 |
0.109 |
0.233 |
| SMC |
5 |
0.098 |
0.114 |
0.073 |
-0.219 |
| SMC |
10 |
0.083 |
0.076 |
0.044 |
0.145 |
| SMC |
15 |
0.071 |
0.071 |
0.034 |
-0.024 |
| SMC |
30 |
0.059 |
0.052 |
0.023 |
0.316 |
| Metro |
2 |
24.161 |
0.141 |
0.109 |
219.664 |
| Metro |
5 |
14.357 |
0.114 |
0.073 |
195.339 |
| Metro |
10 |
10.119 |
0.076 |
0.044 |
229.509 |
| Metro |
15 |
8.089 |
0.071 |
0.034 |
236.741 |
| Metro |
30 |
5.916 |
0.052 |
0.023 |
260.372 |
| DEMetro_Z |
2 |
22.916 |
0.141 |
0.109 |
208.282 |
| DEMetro_Z |
5 |
17.405 |
0.114 |
0.073 |
237.134 |
| DEMetro_Z |
10 |
23.469 |
0.076 |
0.044 |
534.623 |
| DEMetro_Z |
15 |
22.144 |
0.071 |
0.034 |
651.708 |
| DEMetro_Z |
30 |
21.252 |
0.052 |
0.023 |
941.299 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
79.448 |
3.38e-37 |
83.686 |
| HMC |
5 |
59.043 |
5.86e-33 |
69.323 |
| HMC |
10 |
82.996 |
5.51e-37 |
117.814 |
| HMC |
15 |
81.829 |
2.65e-37 |
94.223 |
| HMC |
30 |
133.122 |
4.55e-43 |
193.248 |
| SMC |
2 |
0.676 |
0.502 |
0.183 |
| SMC |
5 |
-1.358 |
0.18 |
-0.315 |
| SMC |
10 |
-0.076 |
0.94 |
-0.022 |
| SMC |
15 |
-0.333 |
0.741 |
-0.086 |
| SMC |
30 |
0.456 |
0.65 |
0.132 |
| Metro |
2 |
33.627 |
5.45e-25 |
79.522 |
| Metro |
5 |
19.618 |
2.38e-18 |
65.918 |
| Metro |
10 |
20.415 |
8.81e-19 |
107.118 |
| Metro |
15 |
19.557 |
2.73e-18 |
82.015 |
| Metro |
30 |
24.596 |
5.43e-21 |
179.603 |
| DEMetro_Z |
2 |
17.178 |
8.95e-17 |
74.369 |
| DEMetro_Z |
5 |
20.905 |
4.36e-19 |
80.421 |
| DEMetro_Z |
10 |
16.148 |
4.93e-16 |
443.844 |
| DEMetro_Z |
15 |
16.470 |
2.94e-16 |
623.115 |
| DEMetro_Z |
30 |
22.834 |
4.39e-20 |
2082.460 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
1.015
|
0.319
|
0.185
|
| Metro_vs_DEMetro_Z |
1
|
-2.864
|
0.00769
|
-0.523
|
| Metro_vs_DEMetro_Z |
2
|
-12.264
|
5.33e-13
|
-2.239
|
| Metro_vs_DEMetro_Z |
3
|
-14.779
|
4.92e-15
|
-2.698
|
| Metro_vs_DEMetro_Z |
4
|
-20.967
|
4.55e-19
|
-3.828
|
| DEMetro_Z_vs_SMC |
0
|
17.197
|
9.4e-17
|
3.140
|
| DEMetro_Z_vs_SMC |
1
|
20.935
|
4.74e-19
|
3.822
|
| DEMetro_Z_vs_SMC |
2
|
16.154
|
4.89e-16
|
2.949
|
| DEMetro_Z_vs_SMC |
3
|
16.465
|
2.96e-16
|
3.006
|
| DEMetro_Z_vs_SMC |
4
|
22.823
|
4.46e-20
|
4.167
|
| HMC_vs_DEMetro_Z |
0
|
2.123
|
0.0424
|
0.388
|
| HMC_vs_DEMetro_Z |
1
|
-2.770
|
0.00969
|
-0.506
|
| HMC_vs_DEMetro_Z |
2
|
-11.788
|
1.4e-12
|
-2.152
|
| HMC_vs_DEMetro_Z |
3
|
-13.735
|
3.18e-14
|
-2.508
|
| HMC_vs_DEMetro_Z |
4
|
-20.790
|
5.73e-19
|
-3.796
|
| HMC_vs_Metro |
0
|
1.642
|
0.111
|
0.300
|
| HMC_vs_Metro |
1
|
0.893
|
0.379
|
0.163
|
| HMC_vs_Metro |
2
|
2.129
|
0.0419
|
0.389
|
| HMC_vs_Metro |
3
|
2.850
|
0.00797
|
0.520
|
| HMC_vs_Metro |
4
|
1.886
|
0.0694
|
0.344
|
| HMC_vs_SMC |
0
|
80.535
|
1.18e-35
|
14.704
|
| HMC_vs_SMC |
1
|
61.095
|
3.39e-32
|
11.154
|
| HMC_vs_SMC |
2
|
80.592
|
1.15e-35
|
14.714
|
| HMC_vs_SMC |
3
|
82.515
|
5.84e-36
|
15.065
|
| HMC_vs_SMC |
4
|
132.386
|
6.73e-42
|
24.170
|
| Metro_vs_SMC |
0
|
33.024
|
1.46e-24
|
6.029
|
| Metro_vs_SMC |
1
|
19.851
|
2.01e-18
|
3.624
|
| Metro_vs_SMC |
2
|
20.169
|
1.31e-18
|
3.682
|
| Metro_vs_SMC |
3
|
19.778
|
2.22e-18
|
3.611
|
| Metro_vs_SMC |
4
|
24.448
|
6.67e-21
|
4.464
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
3.876 |
0.090 |
0.045 |
83.686 |
| HMC |
5 |
2.212 |
0.066 |
0.031 |
69.323 |
| HMC |
10 |
1.581 |
0.050 |
0.013 |
117.814 |
| HMC |
15 |
1.255 |
0.047 |
0.013 |
94.223 |
| HMC |
30 |
0.884 |
0.037 |
0.004 |
193.248 |
| SMC |
2 |
0.098 |
0.090 |
0.045 |
0.183 |
| SMC |
5 |
0.057 |
0.066 |
0.031 |
-0.315 |
| SMC |
10 |
0.050 |
0.050 |
0.013 |
-0.022 |
| SMC |
15 |
0.046 |
0.047 |
0.013 |
-0.086 |
| SMC |
30 |
0.037 |
0.037 |
0.004 |
0.132 |
| Metro |
2 |
3.687 |
0.090 |
0.045 |
79.522 |
| Metro |
5 |
2.107 |
0.066 |
0.031 |
65.918 |
| Metro |
10 |
1.442 |
0.050 |
0.013 |
107.118 |
| Metro |
15 |
1.098 |
0.047 |
0.013 |
82.015 |
| Metro |
30 |
0.824 |
0.037 |
0.004 |
179.603 |
| DEMetro_Z |
2 |
3.454 |
0.090 |
0.045 |
74.369 |
| DEMetro_Z |
5 |
2.556 |
0.066 |
0.031 |
80.421 |
| DEMetro_Z |
10 |
5.817 |
0.050 |
0.013 |
443.844 |
| DEMetro_Z |
15 |
8.033 |
0.047 |
0.013 |
623.115 |
| DEMetro_Z |
30 |
9.168 |
0.037 |
0.004 |
2082.460 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2 |
154.155 |
8.38e-53 |
83.253 |
| HMC |
5 |
175.174 |
2.96e-63 |
70.225 |
| HMC |
10 |
165.744 |
1.09e-50 |
109.890 |
| HMC |
15 |
144.151 |
1.21e-47 |
104.856 |
| HMC |
30 |
149.223 |
8.15e-45 |
195.475 |
| SMC |
2 |
0.921 |
0.361 |
0.253 |
| SMC |
5 |
-1.407 |
0.165 |
-0.332 |
| SMC |
10 |
-0.329 |
0.743 |
-0.092 |
| SMC |
15 |
0.146 |
0.885 |
0.040 |
| SMC |
30 |
0.415 |
0.679 |
0.121 |
| Metro |
2 |
37.714 |
1.81e-26 |
80.674 |
| Metro |
5 |
20.853 |
4.37e-19 |
64.492 |
| Metro |
10 |
21.675 |
1.68e-19 |
100.302 |
| Metro |
15 |
20.293 |
1.02e-18 |
92.933 |
| Metro |
30 |
24.543 |
5.76e-21 |
180.596 |
| DEMetro_Z |
2 |
17.256 |
7.94e-17 |
74.880 |
| DEMetro_Z |
5 |
39.620 |
2.7e-27 |
64.488 |
| DEMetro_Z |
10 |
38.576 |
1.5e-26 |
158.916 |
| DEMetro_Z |
15 |
55.153 |
4.55e-31 |
177.798 |
| DEMetro_Z |
30 |
58.180 |
1.28e-31 |
406.805 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
17.293
|
8.12e-17
|
3.157
|
| DEMetro_Z_vs_SMC |
1
|
39.828
|
7.17e-27
|
7.272
|
| DEMetro_Z_vs_SMC |
2
|
38.982
|
1.32e-26
|
7.117
|
| DEMetro_Z_vs_SMC |
3
|
55.722
|
4.79e-31
|
10.173
|
| DEMetro_Z_vs_SMC |
4
|
57.548
|
1.9e-31
|
10.507
|
| HMC_vs_Metro |
0
|
1.234
|
0.227
|
0.225
|
| HMC_vs_Metro |
1
|
1.899
|
0.0676
|
0.347
|
| HMC_vs_Metro |
2
|
2.127
|
0.0421
|
0.388
|
| HMC_vs_Metro |
3
|
2.580
|
0.0152
|
0.471
|
| HMC_vs_Metro |
4
|
2.003
|
0.0546
|
0.366
|
| Metro_vs_DEMetro_Z |
0
|
1.183
|
0.247
|
0.216
|
| Metro_vs_DEMetro_Z |
1
|
0.001
|
0.999
|
0.000
|
| Metro_vs_DEMetro_Z |
2
|
-9.342
|
3.02e-10
|
-1.706
|
| Metro_vs_DEMetro_Z |
3
|
-18.563
|
1.23e-17
|
-3.389
|
| Metro_vs_DEMetro_Z |
4
|
-23.093
|
3.22e-20
|
-4.216
|
| HMC_vs_SMC |
0
|
162.155
|
1.89e-44
|
29.605
|
| HMC_vs_SMC |
1
|
177.635
|
1.35e-45
|
32.432
|
| HMC_vs_SMC |
2
|
186.273
|
3.41e-46
|
34.009
|
| HMC_vs_SMC |
3
|
152.150
|
1.2e-43
|
27.779
|
| HMC_vs_SMC |
4
|
147.351
|
3.03e-43
|
26.903
|
| Metro_vs_SMC |
0
|
37.161
|
5.16e-26
|
6.785
|
| Metro_vs_SMC |
1
|
21.112
|
3.77e-19
|
3.854
|
| Metro_vs_SMC |
2
|
21.414
|
2.56e-19
|
3.910
|
| Metro_vs_SMC |
3
|
20.548
|
7.88e-19
|
3.752
|
| Metro_vs_SMC |
4
|
24.376
|
7.24e-21
|
4.450
|
| HMC_vs_DEMetro_Z |
0
|
1.858
|
0.0734
|
0.339
|
| HMC_vs_DEMetro_Z |
1
|
3.453
|
0.00173
|
0.630
|
| HMC_vs_DEMetro_Z |
2
|
-11.591
|
2.1e-12
|
-2.116
|
| HMC_vs_DEMetro_Z |
3
|
-22.875
|
4.19e-20
|
-4.176
|
| HMC_vs_DEMetro_Z |
4
|
-31.878
|
3.97e-24
|
-5.820
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2 |
0.617 |
0.012 |
0.007 |
83.253 |
| HMC |
5 |
0.598 |
0.014 |
0.008 |
70.225 |
| HMC |
10 |
0.567 |
0.014 |
0.005 |
109.890 |
| HMC |
15 |
0.537 |
0.014 |
0.005 |
104.856 |
| HMC |
30 |
0.457 |
0.013 |
0.002 |
195.475 |
| SMC |
2 |
0.014 |
0.012 |
0.007 |
0.253 |
| SMC |
5 |
0.012 |
0.014 |
0.008 |
-0.332 |
| SMC |
10 |
0.013 |
0.014 |
0.005 |
-0.092 |
| SMC |
15 |
0.015 |
0.014 |
0.005 |
0.040 |
| SMC |
30 |
0.013 |
0.013 |
0.002 |
0.121 |
| Metro |
2 |
0.599 |
0.012 |
0.007 |
80.674 |
| Metro |
5 |
0.550 |
0.014 |
0.008 |
64.492 |
| Metro |
10 |
0.518 |
0.014 |
0.005 |
100.302 |
| Metro |
15 |
0.477 |
0.014 |
0.005 |
92.933 |
| Metro |
30 |
0.423 |
0.013 |
0.002 |
180.596 |
| DEMetro_Z |
2 |
0.557 |
0.012 |
0.007 |
74.880 |
| DEMetro_Z |
5 |
0.550 |
0.014 |
0.008 |
64.488 |
| DEMetro_Z |
10 |
0.813 |
0.014 |
0.005 |
158.916 |
| DEMetro_Z |
15 |
0.900 |
0.014 |
0.005 |
177.798 |
| DEMetro_Z |
30 |
0.937 |
0.013 |
0.002 |
406.805 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
Mode Transitions (scatter)
KDE + Init Plots
Trace Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Varying_Mode_Distance_with_high_Dimension
(Mixture,
mm,
30 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
4.711 |
5.13e-05 |
5.703 |
| HMC |
8 |
7.325 |
4.5e-08 |
43.075 |
| HMC |
10 |
5.657 |
4.08e-06 |
37.840 |
| HMC |
12 |
4.511 |
9.83e-05 |
35.092 |
| HMC |
15 |
5.868 |
2.27e-06 |
32.457 |
| HMC |
18 |
5.652 |
4.13e-06 |
35.073 |
| SMC |
5 |
1.317 |
0.193 |
0.367 |
| SMC |
8 |
1.839 |
0.0712 |
0.527 |
| SMC |
10 |
1.480 |
0.145 |
0.431 |
| SMC |
12 |
0.792 |
0.431 |
0.217 |
| SMC |
15 |
1.656 |
0.103 |
0.480 |
| SMC |
18 |
1.109 |
0.272 |
0.271 |
| Metro |
5 |
11.035 |
9.89e-13 |
7.333 |
| Metro |
8 |
7.117 |
7.46e-08 |
19.574 |
| Metro |
10 |
6.954 |
1.2e-07 |
43.789 |
| Metro |
12 |
5.660 |
4.05e-06 |
39.588 |
| Metro |
15 |
5.915 |
2e-06 |
34.675 |
| Metro |
18 |
5.811 |
2.66e-06 |
35.599 |
| DEMetro_Z |
5 |
30.134 |
1.94e-23 |
2136.801 |
| DEMetro_Z |
8 |
48.601 |
2.41e-29 |
1287.729 |
| DEMetro_Z |
10 |
37.849 |
3.05e-26 |
962.075 |
| DEMetro_Z |
12 |
42.889 |
8.59e-28 |
767.635 |
| DEMetro_Z |
15 |
52.677 |
2.3e-30 |
474.497 |
| DEMetro_Z |
18 |
46.573 |
7.86e-29 |
399.933 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-30.032
|
2.13e-23
|
-5.483
|
| HMC_vs_DEMetro_Z |
1
|
-46.420
|
9.03e-29
|
-8.475
|
| HMC_vs_DEMetro_Z |
2
|
-36.830
|
6.65e-26
|
-6.724
|
| HMC_vs_DEMetro_Z |
3
|
-40.202
|
5.5e-27
|
-7.340
|
| HMC_vs_DEMetro_Z |
4
|
-39.845
|
7.09e-27
|
-7.275
|
| HMC_vs_DEMetro_Z |
5
|
-41.312
|
2.53e-27
|
-7.542
|
| Metro_vs_SMC |
0
|
10.297
|
3.38e-11
|
1.880
|
| Metro_vs_SMC |
1
|
6.837
|
1.65e-07
|
1.248
|
| Metro_vs_SMC |
2
|
6.811
|
1.77e-07
|
1.244
|
| Metro_vs_SMC |
3
|
5.623
|
4.5e-06
|
1.027
|
| Metro_vs_SMC |
4
|
5.860
|
2.34e-06
|
1.070
|
| Metro_vs_SMC |
5
|
5.829
|
2.55e-06
|
1.064
|
| Metro_vs_DEMetro_Z |
0
|
-30.014
|
2.17e-23
|
-5.480
|
| Metro_vs_DEMetro_Z |
1
|
-48.052
|
3.36e-29
|
-8.773
|
| Metro_vs_DEMetro_Z |
2
|
-34.510
|
4.21e-25
|
-6.301
|
| Metro_vs_DEMetro_Z |
3
|
-39.706
|
7.83e-27
|
-7.249
|
| Metro_vs_DEMetro_Z |
4
|
-38.386
|
2.05e-26
|
-7.008
|
| Metro_vs_DEMetro_Z |
5
|
-41.423
|
2.34e-27
|
-7.563
|
| HMC_vs_Metro |
0
|
-1.191
|
0.243
|
-0.218
|
| HMC_vs_Metro |
1
|
3.288
|
0.00265
|
0.600
|
| HMC_vs_Metro |
2
|
-0.697
|
0.491
|
-0.127
|
| HMC_vs_Metro |
3
|
-0.848
|
0.403
|
-0.155
|
| HMC_vs_Metro |
4
|
-1.313
|
0.2
|
-0.240
|
| HMC_vs_Metro |
5
|
-4.696
|
5.91e-05
|
-0.857
|
| HMC_vs_SMC |
0
|
4.450
|
0.000117
|
0.812
|
| HMC_vs_SMC |
1
|
7.208
|
6.18e-08
|
1.316
|
| HMC_vs_SMC |
2
|
5.567
|
5.25e-06
|
1.016
|
| HMC_vs_SMC |
3
|
4.468
|
0.000111
|
0.816
|
| HMC_vs_SMC |
4
|
5.808
|
2.7e-06
|
1.060
|
| HMC_vs_SMC |
5
|
5.667
|
3.98e-06
|
1.035
|
| DEMetro_Z_vs_SMC |
0
|
30.123
|
1.96e-23
|
5.500
|
| DEMetro_Z_vs_SMC |
1
|
48.715
|
2.27e-29
|
8.894
|
| DEMetro_Z_vs_SMC |
2
|
37.796
|
3.19e-26
|
6.901
|
| DEMetro_Z_vs_SMC |
3
|
42.939
|
8.39e-28
|
7.840
|
| DEMetro_Z_vs_SMC |
4
|
52.548
|
2.58e-30
|
9.594
|
| DEMetro_Z_vs_SMC |
5
|
46.915
|
6.67e-29
|
8.565
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.041 |
0.024 |
0.003 |
5.703 |
| HMC |
8 |
0.254 |
0.026 |
0.005 |
43.075 |
| HMC |
10 |
0.290 |
0.029 |
0.007 |
37.840 |
| HMC |
12 |
0.324 |
0.030 |
0.008 |
35.092 |
| HMC |
15 |
0.469 |
0.035 |
0.013 |
32.457 |
| HMC |
18 |
0.608 |
0.038 |
0.016 |
35.073 |
| SMC |
5 |
0.025 |
0.024 |
0.003 |
0.367 |
| SMC |
8 |
0.029 |
0.026 |
0.005 |
0.527 |
| SMC |
10 |
0.032 |
0.029 |
0.007 |
0.431 |
| SMC |
12 |
0.032 |
0.030 |
0.008 |
0.217 |
| SMC |
15 |
0.041 |
0.035 |
0.013 |
0.480 |
| SMC |
18 |
0.042 |
0.038 |
0.016 |
0.271 |
| Metro |
5 |
0.046 |
0.024 |
0.003 |
7.333 |
| Metro |
8 |
0.130 |
0.026 |
0.005 |
19.574 |
| Metro |
10 |
0.331 |
0.029 |
0.007 |
43.789 |
| Metro |
12 |
0.362 |
0.030 |
0.008 |
39.588 |
| Metro |
15 |
0.499 |
0.035 |
0.013 |
34.675 |
| Metro |
18 |
0.616 |
0.038 |
0.016 |
35.599 |
| DEMetro_Z |
5 |
6.491 |
0.024 |
0.003 |
2136.801 |
| DEMetro_Z |
8 |
6.846 |
0.026 |
0.005 |
1287.729 |
| DEMetro_Z |
10 |
6.663 |
0.029 |
0.007 |
962.075 |
| DEMetro_Z |
12 |
6.473 |
0.030 |
0.008 |
767.635 |
| DEMetro_Z |
15 |
6.389 |
0.035 |
0.013 |
474.497 |
| DEMetro_Z |
18 |
6.536 |
0.038 |
0.016 |
399.933 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
3.285 |
0.00185 |
0.724 |
| HMC |
8 |
4.459 |
0.000114 |
34.579 |
| HMC |
10 |
4.454 |
0.000115 |
29.993 |
| HMC |
12 |
3.487 |
0.00158 |
43.620 |
| HMC |
15 |
4.368 |
0.000146 |
87.346 |
| HMC |
18 |
4.240 |
0.000208 |
143.291 |
| SMC |
5 |
3.757 |
0.000407 |
1.047 |
| SMC |
8 |
2.097 |
0.0404 |
0.534 |
| SMC |
10 |
2.670 |
0.00987 |
0.646 |
| SMC |
12 |
1.840 |
0.071 |
0.504 |
| SMC |
15 |
1.322 |
0.193 |
0.513 |
| SMC |
18 |
3.912 |
0.000348 |
1.775 |
| Metro |
5 |
8.952 |
2.34e-12 |
2.607 |
| Metro |
8 |
5.384 |
8e-06 |
8.232 |
| Metro |
10 |
4.039 |
0.000359 |
34.661 |
| Metro |
12 |
3.887 |
0.000543 |
43.817 |
| Metro |
15 |
4.259 |
0.000197 |
98.969 |
| Metro |
18 |
4.288 |
0.000182 |
144.690 |
| DEMetro_Z |
5 |
41.113 |
2.9e-27 |
18548.245 |
| DEMetro_Z |
8 |
37.363 |
4.42e-26 |
12570.720 |
| DEMetro_Z |
10 |
44.722 |
2.62e-28 |
7070.777 |
| DEMetro_Z |
12 |
36.297 |
1.01e-25 |
5917.856 |
| DEMetro_Z |
15 |
30.907 |
9.5e-24 |
6963.578 |
| DEMetro_Z |
18 |
31.575 |
5.2e-24 |
6662.214 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
-1.558
|
0.13
|
-0.284
|
| HMC_vs_SMC |
1
|
4.398
|
0.000134
|
0.803
|
| HMC_vs_SMC |
2
|
4.377
|
0.000142
|
0.799
|
| HMC_vs_SMC |
3
|
3.445
|
0.00176
|
0.629
|
| HMC_vs_SMC |
4
|
4.330
|
0.000162
|
0.791
|
| HMC_vs_SMC |
5
|
4.191
|
0.000238
|
0.765
|
| Metro_vs_DEMetro_Z |
0
|
-41.113
|
2.9e-27
|
-7.506
|
| Metro_vs_DEMetro_Z |
1
|
-37.318
|
4.58e-26
|
-6.813
|
| Metro_vs_DEMetro_Z |
2
|
-43.651
|
5.25e-28
|
-7.970
|
| Metro_vs_DEMetro_Z |
3
|
-35.415
|
2.02e-25
|
-6.466
|
| Metro_vs_DEMetro_Z |
4
|
-29.641
|
3.08e-23
|
-5.412
|
| Metro_vs_DEMetro_Z |
5
|
-30.026
|
2.15e-23
|
-5.482
|
| HMC_vs_Metro |
0
|
-8.615
|
1.73e-09
|
-1.573
|
| HMC_vs_Metro |
1
|
3.237
|
0.00302
|
0.591
|
| HMC_vs_Metro |
2
|
-0.431
|
0.67
|
-0.079
|
| HMC_vs_Metro |
3
|
-0.021
|
0.983
|
-0.004
|
| HMC_vs_Metro |
4
|
-1.050
|
0.302
|
-0.192
|
| HMC_vs_Metro |
5
|
-2.587
|
0.015
|
-0.472
|
| HMC_vs_DEMetro_Z |
0
|
-41.114
|
2.9e-27
|
-7.506
|
| HMC_vs_DEMetro_Z |
1
|
-37.657
|
3.54e-26
|
-6.875
|
| HMC_vs_DEMetro_Z |
2
|
-44.812
|
2.48e-28
|
-8.182
|
| HMC_vs_DEMetro_Z |
3
|
-35.544
|
1.82e-25
|
-6.489
|
| HMC_vs_DEMetro_Z |
4
|
-29.857
|
2.51e-23
|
-5.451
|
| HMC_vs_DEMetro_Z |
5
|
-30.038
|
2.12e-23
|
-5.484
|
| Metro_vs_SMC |
0
|
4.547
|
8.91e-05
|
0.830
|
| Metro_vs_SMC |
1
|
5.065
|
2.12e-05
|
0.925
|
| Metro_vs_SMC |
2
|
3.963
|
0.000442
|
0.724
|
| Metro_vs_SMC |
3
|
3.838
|
0.00062
|
0.701
|
| Metro_vs_SMC |
4
|
4.237
|
0.000209
|
0.774
|
| Metro_vs_SMC |
5
|
4.239
|
0.000208
|
0.774
|
| DEMetro_Z_vs_SMC |
0
|
41.112
|
2.9e-27
|
7.506
|
| DEMetro_Z_vs_SMC |
1
|
37.365
|
4.42e-26
|
6.822
|
| DEMetro_Z_vs_SMC |
2
|
44.712
|
2.64e-28
|
8.163
|
| DEMetro_Z_vs_SMC |
3
|
36.294
|
1.01e-25
|
6.626
|
| DEMetro_Z_vs_SMC |
4
|
30.902
|
9.54e-24
|
5.642
|
| DEMetro_Z_vs_SMC |
5
|
31.551
|
5.31e-24
|
5.760
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.044 |
0.037 |
0.009 |
0.724 |
| HMC |
8 |
0.510 |
0.044 |
0.013 |
34.579 |
| HMC |
10 |
0.787 |
0.053 |
0.024 |
29.993 |
| HMC |
12 |
1.293 |
0.056 |
0.028 |
43.620 |
| HMC |
15 |
2.082 |
0.058 |
0.023 |
87.346 |
| HMC |
18 |
3.716 |
0.055 |
0.026 |
143.291 |
| SMC |
5 |
0.047 |
0.037 |
0.009 |
1.047 |
| SMC |
8 |
0.051 |
0.044 |
0.013 |
0.534 |
| SMC |
10 |
0.069 |
0.053 |
0.024 |
0.646 |
| SMC |
12 |
0.070 |
0.056 |
0.028 |
0.504 |
| SMC |
15 |
0.070 |
0.058 |
0.023 |
0.513 |
| SMC |
18 |
0.101 |
0.055 |
0.026 |
1.775 |
| Metro |
5 |
0.062 |
0.037 |
0.009 |
2.607 |
| Metro |
8 |
0.155 |
0.044 |
0.013 |
8.232 |
| Metro |
10 |
0.902 |
0.053 |
0.024 |
34.661 |
| Metro |
12 |
1.299 |
0.056 |
0.028 |
43.817 |
| Metro |
15 |
2.352 |
0.058 |
0.023 |
98.969 |
| Metro |
18 |
3.752 |
0.055 |
0.026 |
144.690 |
| DEMetro_Z |
5 |
174.763 |
0.037 |
0.009 |
18548.245 |
| DEMetro_Z |
8 |
169.335 |
0.044 |
0.013 |
12570.720 |
| DEMetro_Z |
10 |
173.254 |
0.053 |
0.024 |
7070.777 |
| DEMetro_Z |
12 |
167.964 |
0.056 |
0.028 |
5917.856 |
| DEMetro_Z |
15 |
161.454 |
0.058 |
0.023 |
6963.578 |
| DEMetro_Z |
18 |
170.256 |
0.055 |
0.026 |
6662.214 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
5.194 |
1.33e-05 |
6.844 |
| HMC |
8 |
7.202 |
6.25e-08 |
55.908 |
| HMC |
10 |
5.745 |
3.2e-06 |
46.885 |
| HMC |
12 |
4.521 |
9.56e-05 |
43.844 |
| HMC |
15 |
5.888 |
2.16e-06 |
40.602 |
| HMC |
18 |
5.713 |
3.5e-06 |
41.869 |
| SMC |
5 |
2.506 |
0.0151 |
0.668 |
| SMC |
8 |
2.693 |
0.00938 |
0.800 |
| SMC |
10 |
2.047 |
0.0455 |
0.595 |
| SMC |
12 |
1.383 |
0.172 |
0.388 |
| SMC |
15 |
2.111 |
0.0394 |
0.634 |
| SMC |
18 |
1.514 |
0.136 |
0.374 |
| Metro |
5 |
12.315 |
7.44e-14 |
9.002 |
| Metro |
8 |
7.078 |
8.46e-08 |
25.662 |
| Metro |
10 |
6.851 |
1.58e-07 |
52.590 |
| Metro |
12 |
5.580 |
5.05e-06 |
50.843 |
| Metro |
15 |
5.985 |
1.65e-06 |
42.794 |
| Metro |
18 |
5.893 |
2.13e-06 |
42.607 |
| DEMetro_Z |
5 |
59.731 |
6.49e-32 |
5564.953 |
| DEMetro_Z |
8 |
71.796 |
3.23e-34 |
3272.028 |
| DEMetro_Z |
10 |
68.698 |
1.15e-33 |
2292.047 |
| DEMetro_Z |
12 |
65.551 |
4.45e-33 |
1905.649 |
| DEMetro_Z |
15 |
60.502 |
4.44e-32 |
1109.462 |
| DEMetro_Z |
18 |
57.260 |
2.16e-31 |
894.223 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-59.633
|
6.81e-32
|
-10.887
|
| Metro_vs_DEMetro_Z |
1
|
-71.250
|
4.04e-34
|
-13.008
|
| Metro_vs_DEMetro_Z |
2
|
-61.312
|
3.06e-32
|
-11.194
|
| Metro_vs_DEMetro_Z |
3
|
-59.302
|
7.99e-32
|
-10.827
|
| Metro_vs_DEMetro_Z |
4
|
-48.594
|
2.44e-29
|
-8.872
|
| Metro_vs_DEMetro_Z |
5
|
-56.316
|
3.53e-31
|
-10.282
|
| DEMetro_Z_vs_SMC |
0
|
59.703
|
6.59e-32
|
10.900
|
| DEMetro_Z_vs_SMC |
1
|
71.777
|
3.27e-34
|
13.105
|
| DEMetro_Z_vs_SMC |
2
|
68.771
|
1.12e-33
|
12.556
|
| DEMetro_Z_vs_SMC |
3
|
65.577
|
4.42e-33
|
11.973
|
| DEMetro_Z_vs_SMC |
4
|
60.593
|
4.3e-32
|
11.063
|
| DEMetro_Z_vs_SMC |
5
|
57.405
|
2.04e-31
|
10.481
|
| HMC_vs_DEMetro_Z |
0
|
-59.673
|
6.68e-32
|
-10.895
|
| HMC_vs_DEMetro_Z |
1
|
-72.999
|
2.01e-34
|
-13.328
|
| HMC_vs_DEMetro_Z |
2
|
-68.703
|
1.15e-33
|
-12.543
|
| HMC_vs_DEMetro_Z |
3
|
-60.868
|
3.78e-32
|
-11.113
|
| HMC_vs_DEMetro_Z |
4
|
-49.163
|
1.74e-29
|
-8.976
|
| HMC_vs_DEMetro_Z |
5
|
-56.482
|
3.25e-31
|
-10.312
|
| HMC_vs_Metro |
0
|
-1.420
|
0.166
|
-0.259
|
| HMC_vs_Metro |
1
|
3.197
|
0.00335
|
0.584
|
| HMC_vs_Metro |
2
|
-0.555
|
0.583
|
-0.101
|
| HMC_vs_Metro |
3
|
-1.038
|
0.308
|
-0.189
|
| HMC_vs_Metro |
4
|
-1.085
|
0.287
|
-0.198
|
| HMC_vs_Metro |
5
|
-1.246
|
0.223
|
-0.228
|
| HMC_vs_SMC |
0
|
4.745
|
5.16e-05
|
0.866
|
| HMC_vs_SMC |
1
|
7.069
|
8.92e-08
|
1.291
|
| HMC_vs_SMC |
2
|
5.641
|
4.29e-06
|
1.030
|
| HMC_vs_SMC |
3
|
4.464
|
0.000112
|
0.815
|
| HMC_vs_SMC |
4
|
5.813
|
2.66e-06
|
1.061
|
| HMC_vs_SMC |
5
|
5.702
|
3.62e-06
|
1.041
|
| Metro_vs_SMC |
0
|
11.210
|
4.65e-12
|
2.047
|
| Metro_vs_SMC |
1
|
6.791
|
1.87e-07
|
1.240
|
| Metro_vs_SMC |
2
|
6.726
|
2.22e-07
|
1.228
|
| Metro_vs_SMC |
3
|
5.527
|
5.87e-06
|
1.009
|
| Metro_vs_SMC |
4
|
5.916
|
2.01e-06
|
1.080
|
| Metro_vs_SMC |
5
|
5.888
|
2.17e-06
|
1.075
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.044 |
0.031 |
0.002 |
6.844 |
| HMC |
8 |
0.206 |
0.033 |
0.003 |
55.908 |
| HMC |
10 |
0.243 |
0.036 |
0.004 |
46.885 |
| HMC |
12 |
0.264 |
0.037 |
0.005 |
43.844 |
| HMC |
15 |
0.391 |
0.042 |
0.009 |
40.602 |
| HMC |
18 |
0.497 |
0.045 |
0.011 |
41.869 |
| SMC |
5 |
0.032 |
0.031 |
0.002 |
0.668 |
| SMC |
8 |
0.036 |
0.033 |
0.003 |
0.800 |
| SMC |
10 |
0.039 |
0.036 |
0.004 |
0.595 |
| SMC |
12 |
0.039 |
0.037 |
0.005 |
0.388 |
| SMC |
15 |
0.047 |
0.042 |
0.009 |
0.634 |
| SMC |
18 |
0.049 |
0.045 |
0.011 |
0.374 |
| Metro |
5 |
0.048 |
0.031 |
0.002 |
9.002 |
| Metro |
8 |
0.112 |
0.033 |
0.003 |
25.662 |
| Metro |
10 |
0.268 |
0.036 |
0.004 |
52.590 |
| Metro |
12 |
0.301 |
0.037 |
0.005 |
50.843 |
| Metro |
15 |
0.410 |
0.042 |
0.009 |
42.794 |
| Metro |
18 |
0.504 |
0.045 |
0.011 |
42.607 |
| DEMetro_Z |
5 |
10.220 |
0.031 |
0.002 |
5564.953 |
| DEMetro_Z |
8 |
10.123 |
0.033 |
0.003 |
3272.028 |
| DEMetro_Z |
10 |
10.144 |
0.036 |
0.004 |
2292.047 |
| DEMetro_Z |
12 |
9.907 |
0.037 |
0.005 |
1905.649 |
| DEMetro_Z |
15 |
9.590 |
0.042 |
0.009 |
1109.462 |
| DEMetro_Z |
18 |
9.686 |
0.045 |
0.011 |
894.223 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
5.085 |
1.76e-05 |
5.833 |
| HMC |
8 |
7.355 |
4.17e-08 |
47.155 |
| HMC |
10 |
5.573 |
5.15e-06 |
44.219 |
| HMC |
12 |
4.506 |
9.98e-05 |
41.267 |
| HMC |
15 |
5.824 |
2.57e-06 |
38.491 |
| HMC |
18 |
5.706 |
3.57e-06 |
41.151 |
| SMC |
5 |
2.902 |
0.00527 |
0.697 |
| SMC |
8 |
3.185 |
0.00233 |
0.834 |
| SMC |
10 |
2.560 |
0.0133 |
0.764 |
| SMC |
12 |
1.488 |
0.142 |
0.386 |
| SMC |
15 |
2.239 |
0.0292 |
0.655 |
| SMC |
18 |
1.901 |
0.0623 |
0.491 |
| Metro |
5 |
11.958 |
7.57e-14 |
7.308 |
| Metro |
8 |
7.228 |
5.6e-08 |
21.280 |
| Metro |
10 |
6.696 |
2.39e-07 |
50.438 |
| Metro |
12 |
5.624 |
4.47e-06 |
46.542 |
| Metro |
15 |
5.859 |
2.34e-06 |
40.942 |
| Metro |
18 |
5.831 |
2.52e-06 |
41.959 |
| DEMetro_Z |
5 |
84.681 |
2.19e-36 |
369.241 |
| DEMetro_Z |
8 |
90.278 |
2.49e-37 |
257.356 |
| DEMetro_Z |
10 |
91.553 |
1.31e-37 |
219.735 |
| DEMetro_Z |
12 |
93.712 |
4.86e-38 |
191.061 |
| DEMetro_Z |
15 |
112.448 |
2.11e-41 |
133.388 |
| DEMetro_Z |
18 |
77.700 |
5.58e-36 |
120.454 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
84.834
|
2.62e-36
|
15.489
|
| DEMetro_Z_vs_SMC |
1
|
90.789
|
3.69e-37
|
16.576
|
| DEMetro_Z_vs_SMC |
2
|
87.293
|
1.15e-36
|
15.937
|
| DEMetro_Z_vs_SMC |
3
|
92.133
|
2.41e-37
|
16.821
|
| DEMetro_Z_vs_SMC |
4
|
106.238
|
3.93e-39
|
19.396
|
| DEMetro_Z_vs_SMC |
5
|
78.639
|
2.34e-35
|
14.357
|
| HMC_vs_Metro |
0
|
-1.132
|
0.267
|
-0.207
|
| HMC_vs_Metro |
1
|
3.355
|
0.00223
|
0.612
|
| HMC_vs_Metro |
2
|
-0.610
|
0.547
|
-0.111
|
| HMC_vs_Metro |
3
|
-0.815
|
0.422
|
-0.149
|
| HMC_vs_Metro |
4
|
-1.117
|
0.273
|
-0.204
|
| HMC_vs_Metro |
5
|
-1.755
|
0.0898
|
-0.320
|
| Metro_vs_DEMetro_Z |
0
|
-77.707
|
3.31e-35
|
-14.187
|
| Metro_vs_DEMetro_Z |
1
|
-56.403
|
3.38e-31
|
-10.298
|
| Metro_vs_DEMetro_Z |
2
|
-20.711
|
6.36e-19
|
-3.781
|
| Metro_vs_DEMetro_Z |
3
|
-17.127
|
1.05e-16
|
-3.127
|
| Metro_vs_DEMetro_Z |
4
|
-13.770
|
2.99e-14
|
-2.514
|
| Metro_vs_DEMetro_Z |
5
|
-11.726
|
1.58e-12
|
-2.141
|
| HMC_vs_SMC |
0
|
4.452
|
0.000116
|
0.813
|
| HMC_vs_SMC |
1
|
7.221
|
5.97e-08
|
1.318
|
| HMC_vs_SMC |
2
|
5.457
|
7.13e-06
|
0.996
|
| HMC_vs_SMC |
3
|
4.450
|
0.000116
|
0.813
|
| HMC_vs_SMC |
4
|
5.743
|
3.23e-06
|
1.048
|
| HMC_vs_SMC |
5
|
5.682
|
3.82e-06
|
1.037
|
| Metro_vs_SMC |
0
|
10.867
|
9.68e-12
|
1.984
|
| Metro_vs_SMC |
1
|
6.894
|
1.42e-07
|
1.259
|
| Metro_vs_SMC |
2
|
6.546
|
3.6e-07
|
1.195
|
| Metro_vs_SMC |
3
|
5.572
|
5.19e-06
|
1.017
|
| Metro_vs_SMC |
4
|
5.789
|
2.84e-06
|
1.057
|
| Metro_vs_SMC |
5
|
5.809
|
2.69e-06
|
1.061
|
| HMC_vs_DEMetro_Z |
0
|
-77.089
|
4.16e-35
|
-14.074
|
| HMC_vs_DEMetro_Z |
1
|
-27.438
|
2.69e-22
|
-5.009
|
| HMC_vs_DEMetro_Z |
2
|
-19.969
|
1.71e-18
|
-3.646
|
| HMC_vs_DEMetro_Z |
3
|
-16.132
|
5.07e-16
|
-2.945
|
| HMC_vs_DEMetro_Z |
4
|
-15.125
|
2.71e-15
|
-2.761
|
| HMC_vs_DEMetro_Z |
5
|
-11.801
|
1.36e-12
|
-2.155
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.023 |
0.014 |
0.002 |
5.833 |
| HMC |
8 |
0.117 |
0.013 |
0.002 |
47.155 |
| HMC |
10 |
0.127 |
0.014 |
0.003 |
44.219 |
| HMC |
12 |
0.133 |
0.013 |
0.003 |
41.267 |
| HMC |
15 |
0.174 |
0.013 |
0.004 |
38.491 |
| HMC |
18 |
0.202 |
0.012 |
0.005 |
41.151 |
| SMC |
5 |
0.015 |
0.014 |
0.002 |
0.697 |
| SMC |
8 |
0.015 |
0.013 |
0.002 |
0.834 |
| SMC |
10 |
0.016 |
0.014 |
0.003 |
0.764 |
| SMC |
12 |
0.014 |
0.013 |
0.003 |
0.386 |
| SMC |
15 |
0.016 |
0.013 |
0.004 |
0.655 |
| SMC |
18 |
0.015 |
0.012 |
0.005 |
0.491 |
| Metro |
5 |
0.025 |
0.014 |
0.002 |
7.308 |
| Metro |
8 |
0.060 |
0.013 |
0.002 |
21.280 |
| Metro |
10 |
0.143 |
0.014 |
0.003 |
50.438 |
| Metro |
12 |
0.149 |
0.013 |
0.003 |
46.542 |
| Metro |
15 |
0.184 |
0.013 |
0.004 |
40.942 |
| Metro |
18 |
0.206 |
0.012 |
0.005 |
41.959 |
| DEMetro_Z |
5 |
0.575 |
0.014 |
0.002 |
369.241 |
| DEMetro_Z |
8 |
0.578 |
0.013 |
0.002 |
257.356 |
| DEMetro_Z |
10 |
0.577 |
0.014 |
0.003 |
219.735 |
| DEMetro_Z |
12 |
0.569 |
0.013 |
0.003 |
191.061 |
| DEMetro_Z |
15 |
0.569 |
0.013 |
0.004 |
133.388 |
| DEMetro_Z |
18 |
0.568 |
0.012 |
0.005 |
120.454 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
3.810 |
0.000619 |
3.907 |
| HMC |
8 |
8.192 |
4.92e-09 |
78.034 |
| HMC |
10 |
261.345 |
1.35e-63 |
128.165 |
| HMC |
12 |
279.061 |
3.06e-67 |
126.233 |
| HMC |
15 |
287.198 |
1.13e-79 |
99.938 |
| HMC |
18 |
276.741 |
2.04e-77 |
98.958 |
| SMC |
5 |
0.055 |
0.956 |
0.014 |
| SMC |
8 |
0.995 |
0.324 |
0.294 |
| SMC |
10 |
0.943 |
0.35 |
0.333 |
| SMC |
12 |
0.316 |
0.753 |
0.083 |
| SMC |
15 |
0.282 |
0.779 |
0.082 |
| SMC |
18 |
-0.577 |
0.567 |
-0.141 |
| Metro |
5 |
9.892 |
1.8e-11 |
6.703 |
| Metro |
8 |
6.390 |
5.35e-07 |
21.036 |
| Metro |
10 |
9.382 |
2.72e-10 |
72.946 |
| Metro |
12 |
16.670 |
2.07e-16 |
109.305 |
| Metro |
15 |
39.615 |
5.12e-27 |
97.488 |
| Metro |
18 |
279.447 |
5e-78 |
99.165 |
| DEMetro_Z |
5 |
21.502 |
2.29e-19 |
3443.156 |
| DEMetro_Z |
8 |
23.698 |
1.58e-20 |
2122.739 |
| DEMetro_Z |
10 |
22.445 |
7.05e-20 |
1644.831 |
| DEMetro_Z |
12 |
22.792 |
4.62e-20 |
1358.805 |
| DEMetro_Z |
15 |
25.249 |
2.72e-21 |
889.869 |
| DEMetro_Z |
18 |
24.064 |
1.03e-20 |
650.555 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-21.427
|
2.52e-19
|
-3.912
|
| HMC_vs_DEMetro_Z |
1
|
-22.816
|
4.49e-20
|
-4.166
|
| HMC_vs_DEMetro_Z |
2
|
-20.702
|
6.44e-19
|
-3.780
|
| HMC_vs_DEMetro_Z |
3
|
-20.618
|
7.19e-19
|
-3.764
|
| HMC_vs_DEMetro_Z |
4
|
-22.478
|
6.77e-20
|
-4.104
|
| HMC_vs_DEMetro_Z |
5
|
-20.411
|
9.45e-19
|
-3.727
|
| Metro_vs_SMC |
0
|
9.805
|
1.03e-10
|
1.790
|
| Metro_vs_SMC |
1
|
6.243
|
8.2e-07
|
1.140
|
| Metro_vs_SMC |
2
|
9.410
|
2.58e-10
|
1.718
|
| Metro_vs_SMC |
3
|
16.759
|
1.86e-16
|
3.060
|
| Metro_vs_SMC |
4
|
40.311
|
5.09e-27
|
7.360
|
| Metro_vs_SMC |
5
|
319.992
|
5.26e-53
|
58.422
|
| Metro_vs_DEMetro_Z |
0
|
-21.478
|
2.36e-19
|
-3.921
|
| Metro_vs_DEMetro_Z |
1
|
-23.200
|
2.84e-20
|
-4.236
|
| Metro_vs_DEMetro_Z |
2
|
-21.939
|
1.32e-19
|
-4.005
|
| Metro_vs_DEMetro_Z |
3
|
-20.581
|
7.54e-19
|
-3.758
|
| Metro_vs_DEMetro_Z |
4
|
-22.391
|
7.53e-20
|
-4.088
|
| Metro_vs_DEMetro_Z |
5
|
-20.410
|
9.47e-19
|
-3.726
|
| HMC_vs_Metro |
0
|
-2.369
|
0.0247
|
-0.432
|
| HMC_vs_Metro |
1
|
5.704
|
3.6e-06
|
1.041
|
| HMC_vs_Metro |
2
|
7.077
|
8.72e-08
|
1.292
|
| HMC_vs_Metro |
3
|
2.563
|
0.0158
|
0.468
|
| HMC_vs_Metro |
4
|
1.013
|
0.319
|
0.185
|
| HMC_vs_Metro |
5
|
-2.072
|
0.0473
|
-0.378
|
| HMC_vs_SMC |
0
|
3.943
|
0.000467
|
0.720
|
| HMC_vs_SMC |
1
|
8.127
|
5.82e-09
|
1.484
|
| HMC_vs_SMC |
2
|
214.572
|
5.65e-48
|
39.175
|
| HMC_vs_SMC |
3
|
264.928
|
1.25e-50
|
48.369
|
| HMC_vs_SMC |
4
|
457.315
|
1.68e-57
|
83.494
|
| HMC_vs_SMC |
5
|
320.388
|
5.08e-53
|
58.494
|
| DEMetro_Z_vs_SMC |
0
|
21.507
|
2.27e-19
|
3.927
|
| DEMetro_Z_vs_SMC |
1
|
23.685
|
1.6e-20
|
4.324
|
| DEMetro_Z_vs_SMC |
2
|
22.438
|
7.11e-20
|
4.097
|
| DEMetro_Z_vs_SMC |
3
|
22.798
|
4.59e-20
|
4.162
|
| DEMetro_Z_vs_SMC |
4
|
25.300
|
2.58e-21
|
4.619
|
| DEMetro_Z_vs_SMC |
5
|
24.036
|
1.07e-20
|
4.388
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.036 |
0.024 |
0.003 |
3.907 |
| HMC |
8 |
0.439 |
0.026 |
0.005 |
78.034 |
| HMC |
10 |
0.913 |
0.029 |
0.007 |
128.165 |
| HMC |
12 |
1.089 |
0.030 |
0.008 |
126.233 |
| HMC |
15 |
1.373 |
0.035 |
0.013 |
99.938 |
| HMC |
18 |
1.646 |
0.038 |
0.016 |
98.958 |
| SMC |
5 |
0.024 |
0.024 |
0.003 |
0.014 |
| SMC |
8 |
0.028 |
0.026 |
0.005 |
0.294 |
| SMC |
10 |
0.032 |
0.029 |
0.007 |
0.333 |
| SMC |
12 |
0.030 |
0.030 |
0.008 |
0.083 |
| SMC |
15 |
0.036 |
0.035 |
0.013 |
0.082 |
| SMC |
18 |
0.036 |
0.038 |
0.016 |
-0.141 |
| Metro |
5 |
0.044 |
0.024 |
0.003 |
6.703 |
| Metro |
8 |
0.137 |
0.026 |
0.005 |
21.036 |
| Metro |
10 |
0.532 |
0.029 |
0.007 |
72.946 |
| Metro |
12 |
0.947 |
0.030 |
0.008 |
109.305 |
| Metro |
15 |
1.340 |
0.035 |
0.013 |
97.488 |
| Metro |
18 |
1.649 |
0.038 |
0.016 |
99.165 |
| DEMetro_Z |
5 |
10.444 |
0.024 |
0.003 |
3443.156 |
| DEMetro_Z |
8 |
11.269 |
0.026 |
0.005 |
2122.739 |
| DEMetro_Z |
10 |
11.371 |
0.029 |
0.007 |
1644.831 |
| DEMetro_Z |
12 |
11.435 |
0.030 |
0.008 |
1358.805 |
| DEMetro_Z |
15 |
11.951 |
0.035 |
0.013 |
889.869 |
| DEMetro_Z |
18 |
10.609 |
0.038 |
0.016 |
650.555 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
4.403 |
5.24e-05 |
0.991 |
| HMC |
8 |
6.452 |
4.64e-07 |
105.806 |
| HMC |
10 |
601.589 |
4.06e-104 |
184.434 |
| HMC |
12 |
850.608 |
1.1e-119 |
229.911 |
| HMC |
15 |
1084.496 |
1.28e-96 |
440.641 |
| HMC |
18 |
1354.342 |
6.25e-98 |
576.282 |
| SMC |
5 |
-0.474 |
0.637 |
-0.114 |
| SMC |
8 |
0.103 |
0.918 |
0.029 |
| SMC |
10 |
0.487 |
0.628 |
0.127 |
| SMC |
12 |
0.859 |
0.394 |
0.236 |
| SMC |
15 |
-0.101 |
0.92 |
-0.031 |
| SMC |
18 |
2.104 |
0.0408 |
0.762 |
| Metro |
5 |
9.854 |
5.35e-14 |
2.560 |
| Metro |
8 |
3.844 |
0.000603 |
9.846 |
| Metro |
10 |
5.984 |
1.66e-06 |
79.346 |
| Metro |
12 |
13.412 |
5.76e-14 |
190.311 |
| Metro |
15 |
31.856 |
3.99e-24 |
427.137 |
| Metro |
18 |
1407.067 |
6.22e-101 |
576.431 |
| DEMetro_Z |
5 |
17.750 |
4.06e-17 |
2140.110 |
| DEMetro_Z |
8 |
15.060 |
3.03e-15 |
1481.650 |
| DEMetro_Z |
10 |
13.088 |
1.07e-13 |
758.951 |
| DEMetro_Z |
12 |
16.910 |
1.47e-16 |
699.594 |
| DEMetro_Z |
15 |
19.614 |
2.78e-18 |
934.961 |
| DEMetro_Z |
18 |
22.720 |
5.04e-20 |
942.511 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
5.906
|
2.06e-06
|
1.078
|
| HMC_vs_SMC |
1
|
6.452
|
4.65e-07
|
1.178
|
| HMC_vs_SMC |
2
|
767.447
|
5.07e-64
|
140.116
|
| HMC_vs_SMC |
3
|
1137.600
|
5.6e-69
|
207.696
|
| HMC_vs_SMC |
4
|
1174.550
|
2.21e-69
|
214.443
|
| HMC_vs_SMC |
5
|
1170.897
|
2.42e-69
|
213.776
|
| Metro_vs_DEMetro_Z |
0
|
-17.725
|
4.22e-17
|
-3.236
|
| Metro_vs_DEMetro_Z |
1
|
-14.891
|
4.05e-15
|
-2.719
|
| Metro_vs_DEMetro_Z |
2
|
-12.076
|
7.77e-13
|
-2.205
|
| Metro_vs_DEMetro_Z |
3
|
-11.671
|
1.77e-12
|
-2.131
|
| Metro_vs_DEMetro_Z |
4
|
-10.721
|
1.33e-11
|
-1.957
|
| Metro_vs_DEMetro_Z |
5
|
-8.810
|
1.08e-09
|
-1.608
|
| HMC_vs_Metro |
0
|
-7.442
|
3.35e-08
|
-1.359
|
| HMC_vs_Metro |
1
|
5.948
|
1.84e-06
|
1.086
|
| HMC_vs_Metro |
2
|
7.897
|
1.04e-08
|
1.442
|
| HMC_vs_Metro |
3
|
2.788
|
0.00926
|
0.509
|
| HMC_vs_Metro |
4
|
1.006
|
0.323
|
0.184
|
| HMC_vs_Metro |
5
|
-2.050
|
0.0495
|
-0.374
|
| HMC_vs_DEMetro_Z |
0
|
-17.743
|
4.1e-17
|
-3.239
|
| HMC_vs_DEMetro_Z |
1
|
-14.025
|
1.88e-14
|
-2.561
|
| HMC_vs_DEMetro_Z |
2
|
-9.881
|
8.65e-11
|
-1.804
|
| HMC_vs_DEMetro_Z |
3
|
-11.348
|
3.48e-12
|
-2.072
|
| HMC_vs_DEMetro_Z |
4
|
-10.375
|
2.85e-11
|
-1.894
|
| HMC_vs_DEMetro_Z |
5
|
-8.813
|
1.07e-09
|
-1.609
|
| Metro_vs_SMC |
0
|
12.808
|
1.83e-13
|
2.338
|
| Metro_vs_SMC |
1
|
3.888
|
0.000542
|
0.710
|
| Metro_vs_SMC |
2
|
5.991
|
1.63e-06
|
1.094
|
| Metro_vs_SMC |
3
|
13.323
|
6.85e-14
|
2.433
|
| Metro_vs_SMC |
4
|
31.947
|
3.74e-24
|
5.833
|
| Metro_vs_SMC |
5
|
1199.469
|
1.2e-69
|
218.992
|
| DEMetro_Z_vs_SMC |
0
|
17.753
|
4.04e-17
|
3.241
|
| DEMetro_Z_vs_SMC |
1
|
15.054
|
3.06e-15
|
2.749
|
| DEMetro_Z_vs_SMC |
2
|
13.076
|
1.09e-13
|
2.387
|
| DEMetro_Z_vs_SMC |
3
|
16.907
|
1.48e-16
|
3.087
|
| DEMetro_Z_vs_SMC |
4
|
19.609
|
2.8e-18
|
3.580
|
| DEMetro_Z_vs_SMC |
5
|
22.678
|
5.31e-20
|
4.140
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.046 |
0.037 |
0.009 |
0.991 |
| HMC |
8 |
1.469 |
0.044 |
0.013 |
105.806 |
| HMC |
10 |
4.571 |
0.053 |
0.024 |
184.434 |
| HMC |
12 |
6.579 |
0.056 |
0.028 |
229.911 |
| HMC |
15 |
10.271 |
0.058 |
0.023 |
440.641 |
| HMC |
18 |
14.778 |
0.055 |
0.026 |
576.282 |
| SMC |
5 |
0.036 |
0.037 |
0.009 |
-0.114 |
| SMC |
8 |
0.044 |
0.044 |
0.013 |
0.029 |
| SMC |
10 |
0.056 |
0.053 |
0.024 |
0.127 |
| SMC |
12 |
0.062 |
0.056 |
0.028 |
0.236 |
| SMC |
15 |
0.057 |
0.058 |
0.023 |
-0.031 |
| SMC |
18 |
0.075 |
0.055 |
0.026 |
0.762 |
| Metro |
5 |
0.061 |
0.037 |
0.009 |
2.560 |
| Metro |
8 |
0.177 |
0.044 |
0.013 |
9.846 |
| Metro |
10 |
1.996 |
0.053 |
0.024 |
79.346 |
| Metro |
12 |
5.455 |
0.056 |
0.028 |
190.311 |
| Metro |
15 |
9.958 |
0.058 |
0.023 |
427.137 |
| Metro |
18 |
14.782 |
0.055 |
0.026 |
576.431 |
| DEMetro_Z |
5 |
20.197 |
0.037 |
0.009 |
2140.110 |
| DEMetro_Z |
8 |
19.998 |
0.044 |
0.013 |
1481.650 |
| DEMetro_Z |
10 |
18.644 |
0.053 |
0.024 |
758.951 |
| DEMetro_Z |
12 |
19.905 |
0.056 |
0.028 |
699.594 |
| DEMetro_Z |
15 |
21.728 |
0.058 |
0.023 |
934.961 |
| DEMetro_Z |
18 |
24.134 |
0.055 |
0.026 |
942.511 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
4.388 |
0.000126 |
4.990 |
| HMC |
8 |
8.023 |
7.54e-09 |
104.981 |
| HMC |
10 |
109.951 |
1.32e-40 |
158.175 |
| HMC |
12 |
103.055 |
1.37e-39 |
162.971 |
| HMC |
15 |
115.848 |
3.93e-42 |
124.914 |
| HMC |
18 |
116.508 |
1.87e-42 |
118.392 |
| SMC |
5 |
-0.158 |
0.875 |
-0.038 |
| SMC |
8 |
1.381 |
0.173 |
0.407 |
| SMC |
10 |
1.236 |
0.223 |
0.446 |
| SMC |
12 |
0.618 |
0.539 |
0.169 |
| SMC |
15 |
0.447 |
0.656 |
0.133 |
| SMC |
18 |
-0.722 |
0.474 |
-0.171 |
| Metro |
5 |
11.058 |
1.26e-12 |
7.977 |
| Metro |
8 |
6.236 |
8.23e-07 |
27.637 |
| Metro |
10 |
9.209 |
4.11e-10 |
89.120 |
| Metro |
12 |
15.772 |
8.98e-16 |
138.795 |
| Metro |
15 |
37.782 |
2.41e-26 |
119.052 |
| Metro |
18 |
97.239 |
2.38e-39 |
121.084 |
| DEMetro_Z |
5 |
21.520 |
2.23e-19 |
4749.342 |
| DEMetro_Z |
8 |
24.709 |
4.97e-21 |
2998.724 |
| DEMetro_Z |
10 |
23.346 |
2.39e-20 |
2137.140 |
| DEMetro_Z |
12 |
23.038 |
3.44e-20 |
1832.174 |
| DEMetro_Z |
15 |
25.202 |
2.87e-21 |
1149.945 |
| DEMetro_Z |
18 |
25.404 |
2.3e-21 |
816.299 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-21.498
|
2.3e-19
|
-3.925
|
| Metro_vs_DEMetro_Z |
1
|
-24.154
|
9.32e-21
|
-4.410
|
| Metro_vs_DEMetro_Z |
2
|
-22.776
|
4.71e-20
|
-4.158
|
| Metro_vs_DEMetro_Z |
3
|
-20.975
|
4.5e-19
|
-3.829
|
| Metro_vs_DEMetro_Z |
4
|
-22.614
|
5.74e-20
|
-4.129
|
| Metro_vs_DEMetro_Z |
5
|
-21.752
|
1.67e-19
|
-3.971
|
| DEMetro_Z_vs_SMC |
0
|
21.522
|
2.23e-19
|
3.929
|
| DEMetro_Z_vs_SMC |
1
|
24.703
|
5e-21
|
4.510
|
| DEMetro_Z_vs_SMC |
2
|
23.337
|
2.41e-20
|
4.261
|
| DEMetro_Z_vs_SMC |
3
|
23.043
|
3.42e-20
|
4.207
|
| DEMetro_Z_vs_SMC |
4
|
25.251
|
2.72e-21
|
4.610
|
| DEMetro_Z_vs_SMC |
5
|
25.381
|
2.36e-21
|
4.634
|
| HMC_vs_DEMetro_Z |
0
|
-21.457
|
2.42e-19
|
-3.917
|
| HMC_vs_DEMetro_Z |
1
|
-23.855
|
1.32e-20
|
-4.355
|
| HMC_vs_DEMetro_Z |
2
|
-21.538
|
2.18e-19
|
-3.932
|
| HMC_vs_DEMetro_Z |
3
|
-20.977
|
4.49e-19
|
-3.830
|
| HMC_vs_DEMetro_Z |
4
|
-22.520
|
6.43e-20
|
-4.112
|
| HMC_vs_DEMetro_Z |
5
|
-21.482
|
2.35e-19
|
-3.922
|
| HMC_vs_Metro |
0
|
-2.253
|
0.032
|
-0.411
|
| HMC_vs_Metro |
1
|
5.716
|
3.48e-06
|
1.044
|
| HMC_vs_Metro |
2
|
6.971
|
1.16e-07
|
1.273
|
| HMC_vs_Metro |
3
|
2.773
|
0.00961
|
0.506
|
| HMC_vs_Metro |
4
|
1.907
|
0.0664
|
0.348
|
| HMC_vs_Metro |
5
|
-1.913
|
0.0657
|
-0.349
|
| HMC_vs_SMC |
0
|
4.504
|
0.0001
|
0.822
|
| HMC_vs_SMC |
1
|
7.975
|
8.54e-09
|
1.456
|
| HMC_vs_SMC |
2
|
102.581
|
1.08e-38
|
18.729
|
| HMC_vs_SMC |
3
|
100.521
|
1.94e-38
|
18.353
|
| HMC_vs_SMC |
4
|
126.833
|
2.33e-41
|
23.156
|
| HMC_vs_SMC |
5
|
117.652
|
2.05e-40
|
21.480
|
| Metro_vs_SMC |
0
|
10.667
|
1.49e-11
|
1.948
|
| Metro_vs_SMC |
1
|
6.092
|
1.24e-06
|
1.112
|
| Metro_vs_SMC |
2
|
9.213
|
4.09e-10
|
1.682
|
| Metro_vs_SMC |
3
|
15.840
|
8.17e-16
|
2.892
|
| Metro_vs_SMC |
4
|
38.121
|
2.5e-26
|
6.960
|
| Metro_vs_SMC |
5
|
96.392
|
6.54e-38
|
17.599
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.040 |
0.031 |
0.002 |
4.990 |
| HMC |
8 |
0.357 |
0.033 |
0.003 |
104.981 |
| HMC |
10 |
0.734 |
0.036 |
0.004 |
158.175 |
| HMC |
12 |
0.881 |
0.037 |
0.005 |
162.971 |
| HMC |
15 |
1.117 |
0.042 |
0.009 |
124.914 |
| HMC |
18 |
1.322 |
0.045 |
0.011 |
118.392 |
| SMC |
5 |
0.031 |
0.031 |
0.002 |
-0.038 |
| SMC |
8 |
0.034 |
0.033 |
0.003 |
0.407 |
| SMC |
10 |
0.038 |
0.036 |
0.004 |
0.446 |
| SMC |
12 |
0.038 |
0.037 |
0.005 |
0.169 |
| SMC |
15 |
0.043 |
0.042 |
0.009 |
0.133 |
| SMC |
18 |
0.043 |
0.045 |
0.011 |
-0.171 |
| Metro |
5 |
0.046 |
0.031 |
0.002 |
7.977 |
| Metro |
8 |
0.118 |
0.033 |
0.003 |
27.637 |
| Metro |
10 |
0.429 |
0.036 |
0.004 |
89.120 |
| Metro |
12 |
0.756 |
0.037 |
0.005 |
138.795 |
| Metro |
15 |
1.066 |
0.042 |
0.009 |
119.052 |
| Metro |
18 |
1.351 |
0.045 |
0.011 |
121.084 |
| DEMetro_Z |
5 |
8.726 |
0.031 |
0.002 |
4749.342 |
| DEMetro_Z |
8 |
9.280 |
0.033 |
0.003 |
2998.724 |
| DEMetro_Z |
10 |
9.461 |
0.036 |
0.004 |
2137.140 |
| DEMetro_Z |
12 |
9.526 |
0.037 |
0.005 |
1832.174 |
| DEMetro_Z |
15 |
9.938 |
0.042 |
0.009 |
1149.945 |
| DEMetro_Z |
18 |
8.846 |
0.045 |
0.011 |
816.299 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
4.316 |
0.000149 |
4.092 |
| HMC |
8 |
8.076 |
6.58e-09 |
86.224 |
| HMC |
10 |
129.905 |
2.35e-43 |
151.738 |
| HMC |
12 |
149.645 |
7.8e-46 |
151.356 |
| HMC |
15 |
149.936 |
1.94e-47 |
118.681 |
| HMC |
18 |
157.556 |
7.71e-49 |
115.430 |
| SMC |
5 |
0.459 |
0.648 |
0.116 |
| SMC |
8 |
1.585 |
0.119 |
0.479 |
| SMC |
10 |
1.305 |
0.198 |
0.470 |
| SMC |
12 |
0.414 |
0.681 |
0.111 |
| SMC |
15 |
0.483 |
0.631 |
0.144 |
| SMC |
18 |
0.011 |
0.991 |
0.003 |
| Metro |
5 |
11.070 |
6.08e-13 |
6.694 |
| Metro |
8 |
6.390 |
5.37e-07 |
22.818 |
| Metro |
10 |
8.901 |
8.58e-10 |
85.186 |
| Metro |
12 |
16.362 |
3.42e-16 |
130.843 |
| Metro |
15 |
38.020 |
1.98e-26 |
116.536 |
| Metro |
18 |
173.441 |
3.13e-51 |
116.105 |
| DEMetro_Z |
5 |
103.321 |
7.61e-39 |
597.219 |
| DEMetro_Z |
8 |
58.098 |
1.35e-31 |
426.373 |
| DEMetro_Z |
10 |
74.027 |
1.12e-34 |
359.262 |
| DEMetro_Z |
12 |
62.775 |
1.34e-32 |
319.588 |
| DEMetro_Z |
15 |
48.073 |
2.87e-29 |
229.826 |
| DEMetro_Z |
18 |
71.248 |
2.39e-34 |
198.777 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
103.114
|
9.31e-39
|
18.826
|
| DEMetro_Z_vs_SMC |
1
|
57.482
|
1.96e-31
|
10.495
|
| DEMetro_Z_vs_SMC |
2
|
72.712
|
2.25e-34
|
13.275
|
| DEMetro_Z_vs_SMC |
3
|
62.236
|
1.99e-32
|
11.363
|
| DEMetro_Z_vs_SMC |
4
|
49.634
|
1.33e-29
|
9.062
|
| DEMetro_Z_vs_SMC |
5
|
71.448
|
3.73e-34
|
13.045
|
| HMC_vs_Metro |
0
|
-2.376
|
0.0243
|
-0.434
|
| HMC_vs_Metro |
1
|
5.707
|
3.57e-06
|
1.042
|
| HMC_vs_Metro |
2
|
6.961
|
1.19e-07
|
1.271
|
| HMC_vs_Metro |
3
|
2.604
|
0.0144
|
0.475
|
| HMC_vs_Metro |
4
|
0.738
|
0.467
|
0.135
|
| HMC_vs_Metro |
5
|
-0.844
|
0.406
|
-0.154
|
| Metro_vs_DEMetro_Z |
0
|
-102.014
|
1.27e-38
|
-18.625
|
| Metro_vs_DEMetro_Z |
1
|
-46.583
|
8.17e-29
|
-8.505
|
| Metro_vs_DEMetro_Z |
2
|
-26.203
|
9.71e-22
|
-4.784
|
| Metro_vs_DEMetro_Z |
3
|
-18.674
|
1.04e-17
|
-3.409
|
| Metro_vs_DEMetro_Z |
4
|
-21.188
|
3.42e-19
|
-3.868
|
| Metro_vs_DEMetro_Z |
5
|
-28.130
|
1.34e-22
|
-5.136
|
| HMC_vs_SMC |
0
|
4.272
|
0.00019
|
0.780
|
| HMC_vs_SMC |
1
|
8.004
|
7.94e-09
|
1.461
|
| HMC_vs_SMC |
2
|
125.531
|
3.14e-41
|
22.919
|
| HMC_vs_SMC |
3
|
147.577
|
2.9e-43
|
26.944
|
| HMC_vs_SMC |
4
|
168.237
|
6.51e-45
|
30.716
|
| HMC_vs_SMC |
5
|
162.326
|
1.84e-44
|
29.637
|
| Metro_vs_SMC |
0
|
10.610
|
1.69e-11
|
1.937
|
| Metro_vs_SMC |
1
|
6.196
|
9.32e-07
|
1.131
|
| Metro_vs_SMC |
2
|
8.910
|
8.46e-10
|
1.627
|
| Metro_vs_SMC |
3
|
16.434
|
3.12e-16
|
3.000
|
| Metro_vs_SMC |
4
|
38.667
|
1.67e-26
|
7.060
|
| Metro_vs_SMC |
5
|
187.865
|
2.66e-46
|
34.299
|
| HMC_vs_DEMetro_Z |
0
|
-96.201
|
6.93e-38
|
-17.564
|
| HMC_vs_DEMetro_Z |
1
|
-27.349
|
2.94e-22
|
-4.993
|
| HMC_vs_DEMetro_Z |
2
|
-41.982
|
1.6e-27
|
-7.665
|
| HMC_vs_DEMetro_Z |
3
|
-32.606
|
2.1e-24
|
-5.953
|
| HMC_vs_DEMetro_Z |
4
|
-23.595
|
1.78e-20
|
-4.308
|
| HMC_vs_DEMetro_Z |
5
|
-30.278
|
1.7e-23
|
-5.528
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.020 |
0.014 |
0.002 |
4.092 |
| HMC |
8 |
0.203 |
0.013 |
0.002 |
86.224 |
| HMC |
10 |
0.402 |
0.014 |
0.003 |
151.738 |
| HMC |
12 |
0.453 |
0.013 |
0.003 |
151.356 |
| HMC |
15 |
0.507 |
0.013 |
0.004 |
118.681 |
| HMC |
18 |
0.544 |
0.012 |
0.005 |
115.430 |
| SMC |
5 |
0.014 |
0.014 |
0.002 |
0.116 |
| SMC |
8 |
0.014 |
0.013 |
0.002 |
0.479 |
| SMC |
10 |
0.015 |
0.014 |
0.003 |
0.470 |
| SMC |
12 |
0.014 |
0.013 |
0.003 |
0.111 |
| SMC |
15 |
0.014 |
0.013 |
0.004 |
0.144 |
| SMC |
18 |
0.012 |
0.012 |
0.005 |
0.003 |
| Metro |
5 |
0.024 |
0.014 |
0.002 |
6.694 |
| Metro |
8 |
0.063 |
0.013 |
0.002 |
22.818 |
| Metro |
10 |
0.232 |
0.014 |
0.003 |
85.186 |
| Metro |
12 |
0.394 |
0.013 |
0.003 |
130.843 |
| Metro |
15 |
0.498 |
0.013 |
0.004 |
116.536 |
| Metro |
18 |
0.548 |
0.012 |
0.005 |
116.105 |
| DEMetro_Z |
5 |
0.921 |
0.014 |
0.002 |
597.219 |
| DEMetro_Z |
8 |
0.949 |
0.013 |
0.002 |
426.373 |
| DEMetro_Z |
10 |
0.934 |
0.014 |
0.003 |
359.262 |
| DEMetro_Z |
12 |
0.942 |
0.013 |
0.003 |
319.588 |
| DEMetro_Z |
15 |
0.970 |
0.013 |
0.004 |
229.826 |
| DEMetro_Z |
18 |
0.929 |
0.012 |
0.005 |
198.777 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
Mode Transitions (scatter)
Trace Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Varying_Mode_Distance_with_high_Correlation
(Mixture,
mm,
30 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
4.991 |
2.58e-05 |
27.386 |
| HMC |
8 |
4.389 |
0.000137 |
16.949 |
| HMC |
10 |
6.465 |
4.4e-07 |
27.401 |
| HMC |
12 |
6.061 |
1.33e-06 |
28.150 |
| HMC |
15 |
7.020 |
9.96e-08 |
29.906 |
| HMC |
18 |
6.993 |
1.05e-07 |
23.508 |
| SMC |
5 |
-0.169 |
0.866 |
-0.053 |
| SMC |
8 |
0.081 |
0.936 |
0.023 |
| SMC |
10 |
-0.410 |
0.684 |
-0.094 |
| SMC |
12 |
-0.599 |
0.552 |
-0.137 |
| SMC |
15 |
1.160 |
0.251 |
0.294 |
| SMC |
18 |
-0.223 |
0.824 |
-0.057 |
| Metro |
5 |
6.294 |
7.02e-07 |
27.919 |
| Metro |
8 |
6.443 |
4.67e-07 |
25.877 |
| Metro |
10 |
6.426 |
4.88e-07 |
24.374 |
| Metro |
12 |
5.090 |
1.96e-05 |
22.125 |
| Metro |
15 |
6.277 |
7.36e-07 |
27.919 |
| Metro |
18 |
6.749 |
2.03e-07 |
24.612 |
| DEMetro_Z |
5 |
7.699 |
1.67e-08 |
27.536 |
| DEMetro_Z |
8 |
6.040 |
1.4e-06 |
22.918 |
| DEMetro_Z |
10 |
6.662 |
2.59e-07 |
28.554 |
| DEMetro_Z |
12 |
7.387 |
3.76e-08 |
27.802 |
| DEMetro_Z |
15 |
6.132 |
1.09e-06 |
26.592 |
| DEMetro_Z |
18 |
6.041 |
1.4e-06 |
24.393 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-0.025
|
0.98
|
-0.005
|
| HMC_vs_DEMetro_Z |
1
|
-1.009
|
0.321
|
-0.184
|
| HMC_vs_DEMetro_Z |
2
|
-0.159
|
0.875
|
-0.029
|
| HMC_vs_DEMetro_Z |
3
|
0.061
|
0.952
|
0.011
|
| HMC_vs_DEMetro_Z |
4
|
0.564
|
0.577
|
0.103
|
| HMC_vs_DEMetro_Z |
5
|
-0.199
|
0.843
|
-0.036
|
| Metro_vs_SMC |
0
|
6.342
|
6.25e-07
|
1.158
|
| Metro_vs_SMC |
1
|
6.361
|
5.94e-07
|
1.161
|
| Metro_vs_SMC |
2
|
6.434
|
4.87e-07
|
1.175
|
| Metro_vs_SMC |
3
|
5.087
|
1.99e-05
|
0.929
|
| Metro_vs_SMC |
4
|
6.140
|
1.09e-06
|
1.121
|
| Metro_vs_SMC |
5
|
6.904
|
1.38e-07
|
1.260
|
| Metro_vs_DEMetro_Z |
0
|
0.059
|
0.953
|
0.011
|
| Metro_vs_DEMetro_Z |
1
|
0.526
|
0.603
|
0.096
|
| Metro_vs_DEMetro_Z |
2
|
-0.670
|
0.508
|
-0.122
|
| Metro_vs_DEMetro_Z |
3
|
-1.006
|
0.323
|
-0.184
|
| Metro_vs_DEMetro_Z |
4
|
0.222
|
0.826
|
0.041
|
| Metro_vs_DEMetro_Z |
5
|
0.047
|
0.963
|
0.009
|
| HMC_vs_Metro |
0
|
-0.072
|
0.943
|
-0.013
|
| HMC_vs_Metro |
1
|
-1.627
|
0.115
|
-0.297
|
| HMC_vs_Metro |
2
|
0.517
|
0.609
|
0.094
|
| HMC_vs_Metro |
3
|
1.461
|
0.155
|
0.267
|
| HMC_vs_Metro |
4
|
0.471
|
0.641
|
0.086
|
| HMC_vs_Metro |
5
|
-0.372
|
0.712
|
-0.068
|
| HMC_vs_SMC |
0
|
4.940
|
3e-05
|
0.902
|
| HMC_vs_SMC |
1
|
4.438
|
0.00012
|
0.810
|
| HMC_vs_SMC |
2
|
6.513
|
3.94e-07
|
1.189
|
| HMC_vs_SMC |
3
|
6.111
|
1.18e-06
|
1.116
|
| HMC_vs_SMC |
4
|
6.841
|
1.63e-07
|
1.249
|
| HMC_vs_SMC |
5
|
7.044
|
9.52e-08
|
1.286
|
| DEMetro_Z_vs_SMC |
0
|
7.740
|
1.55e-08
|
1.413
|
| DEMetro_Z_vs_SMC |
1
|
6.035
|
1.45e-06
|
1.102
|
| DEMetro_Z_vs_SMC |
2
|
6.696
|
2.41e-07
|
1.222
|
| DEMetro_Z_vs_SMC |
3
|
7.428
|
3.48e-08
|
1.356
|
| DEMetro_Z_vs_SMC |
4
|
6.060
|
1.35e-06
|
1.106
|
| DEMetro_Z_vs_SMC |
5
|
6.101
|
1.21e-06
|
1.114
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.527 |
0.035 |
0.018 |
27.386 |
| HMC |
8 |
0.694 |
0.057 |
0.038 |
16.949 |
| HMC |
10 |
1.437 |
0.069 |
0.050 |
27.401 |
| HMC |
12 |
1.945 |
0.084 |
0.066 |
28.150 |
| HMC |
15 |
2.250 |
0.081 |
0.073 |
29.906 |
| HMC |
18 |
2.259 |
0.130 |
0.091 |
23.508 |
| SMC |
5 |
0.034 |
0.035 |
0.018 |
-0.053 |
| SMC |
8 |
0.058 |
0.057 |
0.038 |
0.023 |
| SMC |
10 |
0.065 |
0.069 |
0.050 |
-0.094 |
| SMC |
12 |
0.075 |
0.084 |
0.066 |
-0.137 |
| SMC |
15 |
0.102 |
0.081 |
0.073 |
0.294 |
| SMC |
18 |
0.124 |
0.130 |
0.091 |
-0.057 |
| Metro |
5 |
0.536 |
0.035 |
0.018 |
27.919 |
| Metro |
8 |
1.030 |
0.057 |
0.038 |
25.877 |
| Metro |
10 |
1.286 |
0.069 |
0.050 |
24.374 |
| Metro |
12 |
1.546 |
0.084 |
0.066 |
22.125 |
| Metro |
15 |
2.106 |
0.081 |
0.073 |
27.919 |
| Metro |
18 |
2.359 |
0.130 |
0.091 |
24.612 |
| DEMetro_Z |
5 |
0.529 |
0.035 |
0.018 |
27.536 |
| DEMetro_Z |
8 |
0.919 |
0.057 |
0.038 |
22.918 |
| DEMetro_Z |
10 |
1.495 |
0.069 |
0.050 |
28.554 |
| DEMetro_Z |
12 |
1.922 |
0.084 |
0.066 |
27.802 |
| DEMetro_Z |
15 |
2.010 |
0.081 |
0.073 |
26.592 |
| DEMetro_Z |
18 |
2.339 |
0.130 |
0.091 |
24.393 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
3.587 |
0.00121 |
16.973 |
| HMC |
8 |
3.634 |
0.00107 |
20.425 |
| HMC |
10 |
4.642 |
6.84e-05 |
43.769 |
| HMC |
12 |
4.829 |
4.08e-05 |
80.603 |
| HMC |
15 |
4.833 |
4.03e-05 |
64.602 |
| HMC |
18 |
5.413 |
8.04e-06 |
59.892 |
| SMC |
5 |
-0.837 |
0.406 |
-0.238 |
| SMC |
8 |
-0.203 |
0.84 |
-0.054 |
| SMC |
10 |
-0.252 |
0.802 |
-0.074 |
| SMC |
12 |
0.825 |
0.413 |
0.238 |
| SMC |
15 |
0.286 |
0.776 |
0.073 |
| SMC |
18 |
-0.716 |
0.477 |
-0.170 |
| Metro |
5 |
4.323 |
0.000164 |
17.127 |
| Metro |
8 |
5.262 |
1.22e-05 |
33.967 |
| Metro |
10 |
5.117 |
1.82e-05 |
36.351 |
| Metro |
12 |
4.345 |
0.000156 |
61.776 |
| Metro |
15 |
4.605 |
7.59e-05 |
62.105 |
| Metro |
18 |
5.062 |
2.13e-05 |
69.930 |
| DEMetro_Z |
5 |
5.617 |
4.37e-06 |
12.401 |
| DEMetro_Z |
8 |
4.448 |
0.000117 |
26.843 |
| DEMetro_Z |
10 |
4.833 |
4.02e-05 |
46.497 |
| DEMetro_Z |
12 |
5.073 |
2.07e-05 |
69.218 |
| DEMetro_Z |
15 |
4.574 |
8.26e-05 |
56.724 |
| DEMetro_Z |
18 |
4.454 |
0.000115 |
73.214 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
3.692
|
0.000917
|
0.674
|
| HMC_vs_SMC |
1
|
3.688
|
0.000926
|
0.673
|
| HMC_vs_SMC |
2
|
4.625
|
7.18e-05
|
0.844
|
| HMC_vs_SMC |
3
|
4.801
|
4.41e-05
|
0.877
|
| HMC_vs_SMC |
4
|
4.811
|
4.29e-05
|
0.878
|
| HMC_vs_SMC |
5
|
5.413
|
8.04e-06
|
0.988
|
| Metro_vs_DEMetro_Z |
0
|
1.010
|
0.321
|
0.184
|
| Metro_vs_DEMetro_Z |
1
|
0.784
|
0.439
|
0.143
|
| Metro_vs_DEMetro_Z |
2
|
-0.774
|
0.445
|
-0.141
|
| Metro_vs_DEMetro_Z |
3
|
-0.385
|
0.703
|
-0.070
|
| Metro_vs_DEMetro_Z |
4
|
0.348
|
0.731
|
0.063
|
| Metro_vs_DEMetro_Z |
5
|
-0.185
|
0.854
|
-0.034
|
| HMC_vs_Metro |
0
|
-0.024
|
0.981
|
-0.004
|
| HMC_vs_Metro |
1
|
-1.594
|
0.122
|
-0.291
|
| HMC_vs_Metro |
2
|
0.600
|
0.553
|
0.110
|
| HMC_vs_Metro |
3
|
1.347
|
0.188
|
0.246
|
| HMC_vs_Metro |
4
|
0.189
|
0.851
|
0.035
|
| HMC_vs_Metro |
5
|
-1.005
|
0.323
|
-0.184
|
| HMC_vs_DEMetro_Z |
0
|
0.967
|
0.342
|
0.176
|
| HMC_vs_DEMetro_Z |
1
|
-0.709
|
0.484
|
-0.130
|
| HMC_vs_DEMetro_Z |
2
|
-0.174
|
0.863
|
-0.032
|
| HMC_vs_DEMetro_Z |
3
|
0.525
|
0.603
|
0.096
|
| HMC_vs_DEMetro_Z |
4
|
0.469
|
0.643
|
0.086
|
| HMC_vs_DEMetro_Z |
5
|
-0.915
|
0.368
|
-0.167
|
| Metro_vs_SMC |
0
|
4.368
|
0.000146
|
0.797
|
| Metro_vs_SMC |
1
|
5.241
|
1.3e-05
|
0.957
|
| Metro_vs_SMC |
2
|
5.107
|
1.88e-05
|
0.932
|
| Metro_vs_SMC |
3
|
4.313
|
0.00017
|
0.787
|
| Metro_vs_SMC |
4
|
4.591
|
7.88e-05
|
0.838
|
| Metro_vs_SMC |
5
|
5.059
|
2.15e-05
|
0.924
|
| DEMetro_Z_vs_SMC |
0
|
5.663
|
4.03e-06
|
1.034
|
| DEMetro_Z_vs_SMC |
1
|
4.448
|
0.000117
|
0.812
|
| DEMetro_Z_vs_SMC |
2
|
4.824
|
4.13e-05
|
0.881
|
| DEMetro_Z_vs_SMC |
3
|
5.033
|
2.31e-05
|
0.919
|
| DEMetro_Z_vs_SMC |
4
|
4.589
|
7.93e-05
|
0.838
|
| DEMetro_Z_vs_SMC |
5
|
4.458
|
0.000114
|
0.814
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.824 |
0.080 |
0.044 |
16.973 |
| HMC |
8 |
1.621 |
0.103 |
0.074 |
20.425 |
| HMC |
10 |
4.819 |
0.151 |
0.107 |
43.769 |
| HMC |
12 |
9.223 |
0.156 |
0.112 |
80.603 |
| HMC |
15 |
11.045 |
0.219 |
0.168 |
64.602 |
| HMC |
18 |
11.045 |
0.273 |
0.180 |
59.892 |
| SMC |
5 |
0.070 |
0.080 |
0.044 |
-0.238 |
| SMC |
8 |
0.099 |
0.103 |
0.074 |
-0.054 |
| SMC |
10 |
0.143 |
0.151 |
0.107 |
-0.074 |
| SMC |
12 |
0.183 |
0.156 |
0.112 |
0.238 |
| SMC |
15 |
0.232 |
0.219 |
0.168 |
0.073 |
| SMC |
18 |
0.242 |
0.273 |
0.180 |
-0.170 |
| Metro |
5 |
0.831 |
0.080 |
0.044 |
17.127 |
| Metro |
8 |
2.628 |
0.103 |
0.074 |
33.967 |
| Metro |
10 |
4.028 |
0.151 |
0.107 |
36.351 |
| Metro |
12 |
7.105 |
0.156 |
0.112 |
61.776 |
| Metro |
15 |
10.626 |
0.219 |
0.168 |
62.105 |
| Metro |
18 |
12.851 |
0.273 |
0.180 |
69.930 |
| DEMetro_Z |
5 |
0.624 |
0.080 |
0.044 |
12.401 |
| DEMetro_Z |
8 |
2.098 |
0.103 |
0.074 |
26.843 |
| DEMetro_Z |
10 |
5.110 |
0.151 |
0.107 |
46.497 |
| DEMetro_Z |
12 |
7.942 |
0.156 |
0.112 |
69.218 |
| DEMetro_Z |
15 |
9.724 |
0.219 |
0.168 |
56.724 |
| DEMetro_Z |
18 |
13.442 |
0.273 |
0.180 |
73.214 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
5.015 |
2.42e-05 |
32.795 |
| HMC |
8 |
4.378 |
0.000141 |
20.411 |
| HMC |
10 |
6.689 |
2.41e-07 |
28.442 |
| HMC |
12 |
5.991 |
1.61e-06 |
28.311 |
| HMC |
15 |
7.172 |
6.67e-08 |
33.453 |
| HMC |
18 |
6.852 |
1.54e-07 |
25.662 |
| SMC |
5 |
-0.794 |
0.431 |
-0.236 |
| SMC |
8 |
0.176 |
0.861 |
0.050 |
| SMC |
10 |
-0.265 |
0.792 |
-0.061 |
| SMC |
12 |
-0.477 |
0.635 |
-0.106 |
| SMC |
15 |
1.290 |
0.202 |
0.329 |
| SMC |
18 |
-0.578 |
0.566 |
-0.146 |
| Metro |
5 |
6.379 |
5.61e-07 |
34.298 |
| Metro |
8 |
6.839 |
1.61e-07 |
30.274 |
| Metro |
10 |
6.922 |
1.28e-07 |
25.467 |
| Metro |
12 |
5.221 |
1.36e-05 |
22.052 |
| Metro |
15 |
6.313 |
6.69e-07 |
32.605 |
| Metro |
18 |
7.130 |
7.39e-08 |
26.602 |
| DEMetro_Z |
5 |
7.873 |
1.08e-08 |
32.631 |
| DEMetro_Z |
8 |
6.064 |
1.32e-06 |
27.504 |
| DEMetro_Z |
10 |
6.664 |
2.58e-07 |
29.261 |
| DEMetro_Z |
12 |
7.382 |
3.81e-08 |
27.990 |
| DEMetro_Z |
15 |
6.058 |
1.35e-06 |
31.549 |
| DEMetro_Z |
18 |
6.011 |
1.52e-06 |
26.324 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
0.220
|
0.827
|
0.040
|
| Metro_vs_DEMetro_Z |
1
|
0.433
|
0.668
|
0.079
|
| Metro_vs_DEMetro_Z |
2
|
-0.606
|
0.549
|
-0.111
|
| Metro_vs_DEMetro_Z |
3
|
-1.070
|
0.293
|
-0.195
|
| Metro_vs_DEMetro_Z |
4
|
0.149
|
0.883
|
0.027
|
| Metro_vs_DEMetro_Z |
5
|
0.054
|
0.957
|
0.010
|
| DEMetro_Z_vs_SMC |
0
|
7.933
|
9.48e-09
|
1.448
|
| DEMetro_Z_vs_SMC |
1
|
6.046
|
1.4e-06
|
1.104
|
| DEMetro_Z_vs_SMC |
2
|
6.685
|
2.48e-07
|
1.220
|
| DEMetro_Z_vs_SMC |
3
|
7.413
|
3.61e-08
|
1.353
|
| DEMetro_Z_vs_SMC |
4
|
5.992
|
1.63e-06
|
1.094
|
| DEMetro_Z_vs_SMC |
5
|
6.077
|
1.29e-06
|
1.110
|
| HMC_vs_DEMetro_Z |
0
|
0.024
|
0.981
|
0.004
|
| HMC_vs_DEMetro_Z |
1
|
-1.002
|
0.324
|
-0.183
|
| HMC_vs_DEMetro_Z |
2
|
-0.111
|
0.912
|
-0.020
|
| HMC_vs_DEMetro_Z |
3
|
0.054
|
0.957
|
0.010
|
| HMC_vs_DEMetro_Z |
4
|
0.291
|
0.773
|
0.053
|
| HMC_vs_DEMetro_Z |
5
|
-0.135
|
0.893
|
-0.025
|
| HMC_vs_Metro |
0
|
-0.167
|
0.869
|
-0.030
|
| HMC_vs_Metro |
1
|
-1.550
|
0.132
|
-0.283
|
| HMC_vs_Metro |
2
|
0.509
|
0.615
|
0.093
|
| HMC_vs_Metro |
3
|
1.448
|
0.158
|
0.264
|
| HMC_vs_Metro |
4
|
0.169
|
0.867
|
0.031
|
| HMC_vs_Metro |
5
|
-0.278
|
0.783
|
-0.051
|
| HMC_vs_SMC |
0
|
5.020
|
2.4e-05
|
0.917
|
| HMC_vs_SMC |
1
|
4.427
|
0.000124
|
0.808
|
| HMC_vs_SMC |
2
|
6.697
|
2.4e-07
|
1.223
|
| HMC_vs_SMC |
3
|
6.024
|
1.49e-06
|
1.100
|
| HMC_vs_SMC |
4
|
6.982
|
1.12e-07
|
1.275
|
| HMC_vs_SMC |
5
|
6.918
|
1.33e-07
|
1.263
|
| Metro_vs_SMC |
0
|
6.445
|
4.74e-07
|
1.177
|
| Metro_vs_SMC |
1
|
6.742
|
2.13e-07
|
1.231
|
| Metro_vs_SMC |
2
|
6.914
|
1.35e-07
|
1.262
|
| Metro_vs_SMC |
3
|
5.203
|
1.44e-05
|
0.950
|
| Metro_vs_SMC |
4
|
6.191
|
9.44e-07
|
1.130
|
| Metro_vs_SMC |
5
|
7.326
|
4.54e-08
|
1.337
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.485 |
0.048 |
0.013 |
32.795 |
| HMC |
8 |
0.662 |
0.065 |
0.029 |
20.411 |
| HMC |
10 |
1.305 |
0.080 |
0.043 |
28.442 |
| HMC |
12 |
1.764 |
0.093 |
0.059 |
28.311 |
| HMC |
15 |
2.005 |
0.092 |
0.057 |
33.453 |
| HMC |
18 |
2.073 |
0.136 |
0.075 |
25.662 |
| SMC |
5 |
0.045 |
0.048 |
0.013 |
-0.236 |
| SMC |
8 |
0.067 |
0.065 |
0.029 |
0.050 |
| SMC |
10 |
0.077 |
0.080 |
0.043 |
-0.061 |
| SMC |
12 |
0.087 |
0.093 |
0.059 |
-0.106 |
| SMC |
15 |
0.110 |
0.092 |
0.057 |
0.329 |
| SMC |
18 |
0.125 |
0.136 |
0.075 |
-0.146 |
| Metro |
5 |
0.505 |
0.048 |
0.013 |
34.298 |
| Metro |
8 |
0.950 |
0.065 |
0.029 |
30.274 |
| Metro |
10 |
1.177 |
0.080 |
0.043 |
25.467 |
| Metro |
12 |
1.394 |
0.093 |
0.059 |
22.052 |
| Metro |
15 |
1.956 |
0.092 |
0.057 |
32.605 |
| Metro |
18 |
2.144 |
0.136 |
0.075 |
26.602 |
| DEMetro_Z |
5 |
0.482 |
0.048 |
0.013 |
32.631 |
| DEMetro_Z |
8 |
0.869 |
0.065 |
0.029 |
27.504 |
| DEMetro_Z |
10 |
1.340 |
0.080 |
0.043 |
29.261 |
| DEMetro_Z |
12 |
1.745 |
0.093 |
0.059 |
27.990 |
| DEMetro_Z |
15 |
1.896 |
0.092 |
0.057 |
31.549 |
| DEMetro_Z |
18 |
2.123 |
0.136 |
0.075 |
26.324 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
4.850 |
3.83e-05 |
32.963 |
| HMC |
8 |
4.431 |
0.000122 |
19.736 |
| HMC |
10 |
6.661 |
2.61e-07 |
31.161 |
| HMC |
12 |
6.158 |
1.02e-06 |
33.185 |
| HMC |
15 |
7.255 |
5.37e-08 |
35.324 |
| HMC |
18 |
7.119 |
7.63e-08 |
28.310 |
| SMC |
5 |
-0.498 |
0.621 |
-0.161 |
| SMC |
8 |
0.147 |
0.883 |
0.041 |
| SMC |
10 |
-0.642 |
0.523 |
-0.144 |
| SMC |
12 |
-0.582 |
0.563 |
-0.130 |
| SMC |
15 |
1.303 |
0.198 |
0.323 |
| SMC |
18 |
-0.466 |
0.643 |
-0.121 |
| Metro |
5 |
6.228 |
8.44e-07 |
33.566 |
| Metro |
8 |
6.803 |
1.78e-07 |
30.158 |
| Metro |
10 |
6.735 |
2.12e-07 |
27.725 |
| Metro |
12 |
5.342 |
9.71e-06 |
25.932 |
| Metro |
15 |
6.463 |
4.45e-07 |
33.027 |
| Metro |
18 |
7.066 |
8.79e-08 |
29.684 |
| DEMetro_Z |
5 |
7.628 |
2.02e-08 |
32.467 |
| DEMetro_Z |
8 |
6.026 |
1.46e-06 |
26.773 |
| DEMetro_Z |
10 |
6.879 |
1.45e-07 |
32.087 |
| DEMetro_Z |
12 |
7.610 |
2.12e-08 |
32.924 |
| DEMetro_Z |
15 |
6.312 |
6.71e-07 |
31.420 |
| DEMetro_Z |
18 |
6.210 |
8.85e-07 |
29.056 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
7.645
|
1.98e-08
|
1.396
|
| DEMetro_Z_vs_SMC |
1
|
6.004
|
1.57e-06
|
1.096
|
| DEMetro_Z_vs_SMC |
2
|
6.913
|
1.35e-07
|
1.262
|
| DEMetro_Z_vs_SMC |
3
|
7.645
|
1.99e-08
|
1.396
|
| DEMetro_Z_vs_SMC |
4
|
6.237
|
8.34e-07
|
1.139
|
| DEMetro_Z_vs_SMC |
5
|
6.275
|
7.52e-07
|
1.146
|
| HMC_vs_Metro |
0
|
-0.065
|
0.949
|
-0.012
|
| HMC_vs_Metro |
1
|
-1.682
|
0.103
|
-0.307
|
| HMC_vs_Metro |
2
|
0.529
|
0.601
|
0.097
|
| HMC_vs_Metro |
3
|
1.534
|
0.136
|
0.280
|
| HMC_vs_Metro |
4
|
0.484
|
0.632
|
0.088
|
| HMC_vs_Metro |
5
|
-0.392
|
0.698
|
-0.072
|
| Metro_vs_DEMetro_Z |
0
|
0.144
|
0.886
|
0.026
|
| Metro_vs_DEMetro_Z |
1
|
0.530
|
0.6
|
0.097
|
| Metro_vs_DEMetro_Z |
2
|
-0.646
|
0.523
|
-0.118
|
| Metro_vs_DEMetro_Z |
3
|
-1.082
|
0.288
|
-0.198
|
| Metro_vs_DEMetro_Z |
4
|
0.231
|
0.819
|
0.042
|
| Metro_vs_DEMetro_Z |
5
|
0.113
|
0.911
|
0.021
|
| HMC_vs_SMC |
0
|
4.842
|
3.93e-05
|
0.884
|
| HMC_vs_SMC |
1
|
4.486
|
0.000106
|
0.819
|
| HMC_vs_SMC |
2
|
6.696
|
2.41e-07
|
1.222
|
| HMC_vs_SMC |
3
|
6.180
|
9.73e-07
|
1.128
|
| HMC_vs_SMC |
4
|
7.080
|
8.66e-08
|
1.293
|
| HMC_vs_SMC |
5
|
7.173
|
6.77e-08
|
1.310
|
| Metro_vs_SMC |
0
|
6.288
|
7.25e-07
|
1.148
|
| Metro_vs_SMC |
1
|
6.712
|
2.3e-07
|
1.225
|
| Metro_vs_SMC |
2
|
6.761
|
2.02e-07
|
1.234
|
| Metro_vs_SMC |
3
|
5.333
|
1e-05
|
0.974
|
| Metro_vs_SMC |
4
|
6.335
|
6.39e-07
|
1.157
|
| Metro_vs_SMC |
5
|
7.205
|
6.23e-08
|
1.315
|
| HMC_vs_DEMetro_Z |
0
|
0.068
|
0.946
|
0.012
|
| HMC_vs_DEMetro_Z |
1
|
-1.022
|
0.315
|
-0.187
|
| HMC_vs_DEMetro_Z |
2
|
-0.117
|
0.908
|
-0.021
|
| HMC_vs_DEMetro_Z |
3
|
0.039
|
0.969
|
0.007
|
| HMC_vs_DEMetro_Z |
4
|
0.586
|
0.563
|
0.107
|
| HMC_vs_DEMetro_Z |
5
|
-0.140
|
0.89
|
-0.026
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.158 |
0.012 |
0.004 |
32.963 |
| HMC |
8 |
0.151 |
0.012 |
0.007 |
19.736 |
| HMC |
10 |
0.261 |
0.012 |
0.008 |
31.161 |
| HMC |
12 |
0.294 |
0.012 |
0.008 |
33.185 |
| HMC |
15 |
0.275 |
0.010 |
0.008 |
35.324 |
| HMC |
18 |
0.236 |
0.012 |
0.008 |
28.310 |
| SMC |
5 |
0.012 |
0.012 |
0.004 |
-0.161 |
| SMC |
8 |
0.012 |
0.012 |
0.007 |
0.041 |
| SMC |
10 |
0.011 |
0.012 |
0.008 |
-0.144 |
| SMC |
12 |
0.011 |
0.012 |
0.008 |
-0.130 |
| SMC |
15 |
0.012 |
0.010 |
0.008 |
0.323 |
| SMC |
18 |
0.012 |
0.012 |
0.008 |
-0.121 |
| Metro |
5 |
0.160 |
0.012 |
0.004 |
33.566 |
| Metro |
8 |
0.225 |
0.012 |
0.007 |
30.158 |
| Metro |
10 |
0.234 |
0.012 |
0.008 |
27.725 |
| Metro |
12 |
0.232 |
0.012 |
0.008 |
25.932 |
| Metro |
15 |
0.258 |
0.010 |
0.008 |
33.027 |
| Metro |
18 |
0.247 |
0.012 |
0.008 |
29.684 |
| DEMetro_Z |
5 |
0.155 |
0.012 |
0.004 |
32.467 |
| DEMetro_Z |
8 |
0.201 |
0.012 |
0.007 |
26.773 |
| DEMetro_Z |
10 |
0.268 |
0.012 |
0.008 |
32.087 |
| DEMetro_Z |
12 |
0.292 |
0.012 |
0.008 |
32.924 |
| DEMetro_Z |
15 |
0.246 |
0.010 |
0.008 |
31.420 |
| DEMetro_Z |
18 |
0.242 |
0.012 |
0.008 |
29.056 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
238.377 |
1.37e-68 |
96.579 |
| HMC |
8 |
264.530 |
1.66e-89 |
73.843 |
| HMC |
10 |
252.096 |
7.91e-89 |
69.309 |
| HMC |
12 |
253.339 |
1.82e-89 |
62.836 |
| HMC |
15 |
253.464 |
8.72e-88 |
71.980 |
| HMC |
18 |
239.838 |
4.57e-86 |
68.719 |
| SMC |
5 |
1.254 |
0.215 |
0.387 |
| SMC |
8 |
-0.915 |
0.364 |
-0.224 |
| SMC |
10 |
0.135 |
0.893 |
0.033 |
| SMC |
12 |
-0.871 |
0.388 |
-0.201 |
| SMC |
15 |
1.321 |
0.192 |
0.336 |
| SMC |
18 |
-1.196 |
0.237 |
-0.289 |
| Metro |
5 |
8.589 |
1.81e-09 |
48.019 |
| Metro |
8 |
167.881 |
2.49e-59 |
73.751 |
| Metro |
10 |
156.539 |
7.77e-58 |
69.372 |
| Metro |
12 |
188.862 |
3.18e-73 |
62.704 |
| Metro |
15 |
219.538 |
3.86e-77 |
72.016 |
| Metro |
18 |
222.317 |
4e-80 |
69.321 |
| DEMetro_Z |
5 |
9.473 |
2.2e-10 |
70.133 |
| DEMetro_Z |
8 |
17.039 |
1.09e-16 |
66.917 |
| DEMetro_Z |
10 |
17.696 |
3.89e-17 |
62.756 |
| DEMetro_Z |
12 |
244.225 |
4.58e-89 |
62.752 |
| DEMetro_Z |
15 |
252.674 |
1.58e-87 |
72.071 |
| DEMetro_Z |
18 |
250.134 |
1.07e-88 |
68.630 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
3.632
|
0.00108
|
0.663
|
| HMC_vs_DEMetro_Z |
1
|
1.752
|
0.0904
|
0.320
|
| HMC_vs_DEMetro_Z |
2
|
1.877
|
0.0706
|
0.343
|
| HMC_vs_DEMetro_Z |
3
|
0.527
|
0.602
|
0.096
|
| HMC_vs_DEMetro_Z |
4
|
-0.331
|
0.743
|
-0.060
|
| HMC_vs_DEMetro_Z |
5
|
0.382
|
0.705
|
0.070
|
| Metro_vs_SMC |
0
|
8.420
|
2.8e-09
|
1.537
|
| Metro_vs_SMC |
1
|
156.480
|
5.31e-44
|
28.569
|
| Metro_vs_SMC |
2
|
171.414
|
3.79e-45
|
31.296
|
| Metro_vs_SMC |
3
|
200.900
|
3.81e-47
|
36.679
|
| Metro_vs_SMC |
4
|
207.986
|
1.4e-47
|
37.973
|
| Metro_vs_SMC |
5
|
260.440
|
2.06e-50
|
47.550
|
| Metro_vs_DEMetro_Z |
0
|
-2.444
|
0.0208
|
-0.446
|
| Metro_vs_DEMetro_Z |
1
|
1.721
|
0.0958
|
0.314
|
| Metro_vs_DEMetro_Z |
2
|
1.857
|
0.0735
|
0.339
|
| Metro_vs_DEMetro_Z |
3
|
-0.233
|
0.817
|
-0.043
|
| Metro_vs_DEMetro_Z |
4
|
-0.195
|
0.847
|
-0.036
|
| Metro_vs_DEMetro_Z |
5
|
2.752
|
0.0101
|
0.502
|
| HMC_vs_Metro |
0
|
8.533
|
2.12e-09
|
1.558
|
| HMC_vs_Metro |
1
|
0.192
|
0.849
|
0.035
|
| HMC_vs_Metro |
2
|
-0.175
|
0.862
|
-0.032
|
| HMC_vs_Metro |
3
|
0.683
|
0.5
|
0.125
|
| HMC_vs_Metro |
4
|
-0.158
|
0.876
|
-0.029
|
| HMC_vs_Metro |
5
|
-3.076
|
0.00454
|
-0.562
|
| HMC_vs_SMC |
0
|
213.653
|
6.4e-48
|
39.007
|
| HMC_vs_SMC |
1
|
284.129
|
1.65e-51
|
51.875
|
| HMC_vs_SMC |
2
|
242.299
|
1.67e-49
|
44.237
|
| HMC_vs_SMC |
3
|
285.437
|
1.44e-51
|
52.113
|
| HMC_vs_SMC |
4
|
248.742
|
7.8e-50
|
45.414
|
| HMC_vs_SMC |
5
|
226.574
|
1.17e-48
|
41.367
|
| DEMetro_Z_vs_SMC |
0
|
9.424
|
2.49e-10
|
1.721
|
| DEMetro_Z_vs_SMC |
1
|
17.114
|
1.07e-16
|
3.125
|
| DEMetro_Z_vs_SMC |
2
|
17.660
|
4.65e-17
|
3.224
|
| DEMetro_Z_vs_SMC |
3
|
251.200
|
5.87e-50
|
45.863
|
| DEMetro_Z_vs_SMC |
4
|
231.116
|
6.57e-49
|
42.196
|
| DEMetro_Z_vs_SMC |
5
|
265.224
|
1.21e-50
|
48.423
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
1.769 |
0.035 |
0.018 |
96.579 |
| HMC |
8 |
2.832 |
0.057 |
0.038 |
73.843 |
| HMC |
10 |
3.529 |
0.069 |
0.050 |
69.309 |
| HMC |
12 |
4.237 |
0.084 |
0.066 |
62.836 |
| HMC |
15 |
5.303 |
0.081 |
0.073 |
71.980 |
| HMC |
18 |
6.353 |
0.130 |
0.091 |
68.719 |
| SMC |
5 |
0.042 |
0.035 |
0.018 |
0.387 |
| SMC |
8 |
0.049 |
0.057 |
0.038 |
-0.224 |
| SMC |
10 |
0.071 |
0.069 |
0.050 |
0.033 |
| SMC |
12 |
0.071 |
0.084 |
0.066 |
-0.201 |
| SMC |
15 |
0.105 |
0.081 |
0.073 |
0.336 |
| SMC |
18 |
0.104 |
0.130 |
0.091 |
-0.289 |
| Metro |
5 |
0.897 |
0.035 |
0.018 |
48.019 |
| Metro |
8 |
2.829 |
0.057 |
0.038 |
73.751 |
| Metro |
10 |
3.532 |
0.069 |
0.050 |
69.372 |
| Metro |
12 |
4.228 |
0.084 |
0.066 |
62.704 |
| Metro |
15 |
5.305 |
0.081 |
0.073 |
72.016 |
| Metro |
18 |
6.407 |
0.130 |
0.091 |
69.321 |
| DEMetro_Z |
5 |
1.294 |
0.035 |
0.018 |
70.133 |
| DEMetro_Z |
8 |
2.572 |
0.057 |
0.038 |
66.917 |
| DEMetro_Z |
10 |
3.202 |
0.069 |
0.050 |
62.756 |
| DEMetro_Z |
12 |
4.231 |
0.084 |
0.066 |
62.752 |
| DEMetro_Z |
15 |
5.309 |
0.081 |
0.073 |
72.071 |
| DEMetro_Z |
18 |
6.345 |
0.130 |
0.091 |
68.630 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
277.842 |
1.55e-77 |
99.283 |
| HMC |
8 |
526.307 |
3.63e-105 |
150.829 |
| HMC |
10 |
603.284 |
8.81e-111 |
164.617 |
| HMC |
12 |
708.821 |
1.68e-105 |
224.612 |
| HMC |
15 |
762.698 |
5.49e-109 |
235.868 |
| HMC |
18 |
1100.035 |
9.04e-123 |
316.837 |
| SMC |
5 |
-0.513 |
0.61 |
-0.131 |
| SMC |
8 |
0.909 |
0.367 |
0.253 |
| SMC |
10 |
-0.590 |
0.558 |
-0.148 |
| SMC |
12 |
-0.010 |
0.992 |
-0.003 |
| SMC |
15 |
-0.726 |
0.471 |
-0.171 |
| SMC |
18 |
-1.400 |
0.167 |
-0.359 |
| Metro |
5 |
5.945 |
1.84e-06 |
35.112 |
| Metro |
8 |
418.388 |
2.3e-85 |
150.911 |
| Metro |
10 |
550.854 |
8.16e-104 |
164.485 |
| Metro |
12 |
661.417 |
7.45e-99 |
224.697 |
| Metro |
15 |
718.606 |
3.67e-103 |
235.918 |
| Metro |
18 |
1090.493 |
5.72e-122 |
316.841 |
| DEMetro_Z |
5 |
8.820 |
1.04e-09 |
70.270 |
| DEMetro_Z |
8 |
16.467 |
2.9e-16 |
136.131 |
| DEMetro_Z |
10 |
16.398 |
3.25e-16 |
148.377 |
| DEMetro_Z |
12 |
704.842 |
5.89e-105 |
224.606 |
| DEMetro_Z |
15 |
774.113 |
1.87e-110 |
235.774 |
| DEMetro_Z |
18 |
1095.099 |
2.25e-122 |
316.770 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
330.485
|
2.06e-53
|
60.338
|
| HMC_vs_SMC |
1
|
709.611
|
4.92e-63
|
129.557
|
| HMC_vs_SMC |
2
|
856.690
|
2.09e-65
|
156.409
|
| HMC_vs_SMC |
3
|
509.166
|
7.45e-59
|
92.961
|
| HMC_vs_SMC |
4
|
752.529
|
8.96e-64
|
137.392
|
| HMC_vs_SMC |
5
|
927.348
|
2.1e-66
|
169.310
|
| Metro_vs_DEMetro_Z |
0
|
-3.546
|
0.00135
|
-0.647
|
| Metro_vs_DEMetro_Z |
1
|
1.782
|
0.0852
|
0.325
|
| Metro_vs_DEMetro_Z |
2
|
1.788
|
0.0842
|
0.326
|
| Metro_vs_DEMetro_Z |
3
|
0.654
|
0.518
|
0.119
|
| Metro_vs_DEMetro_Z |
4
|
1.419
|
0.167
|
0.259
|
| Metro_vs_DEMetro_Z |
5
|
0.760
|
0.454
|
0.139
|
| HMC_vs_Metro |
0
|
11.005
|
7.2e-12
|
2.009
|
| HMC_vs_Metro |
1
|
-0.348
|
0.731
|
-0.063
|
| HMC_vs_Metro |
2
|
0.737
|
0.467
|
0.135
|
| HMC_vs_Metro |
3
|
-0.652
|
0.519
|
-0.119
|
| HMC_vs_Metro |
4
|
-0.521
|
0.606
|
-0.095
|
| HMC_vs_Metro |
5
|
-0.038
|
0.97
|
-0.007
|
| HMC_vs_DEMetro_Z |
0
|
3.661
|
0.000995
|
0.668
|
| HMC_vs_DEMetro_Z |
1
|
1.779
|
0.0857
|
0.325
|
| HMC_vs_DEMetro_Z |
2
|
1.789
|
0.084
|
0.327
|
| HMC_vs_DEMetro_Z |
3
|
0.082
|
0.935
|
0.015
|
| HMC_vs_DEMetro_Z |
4
|
1.850
|
0.0745
|
0.338
|
| HMC_vs_DEMetro_Z |
5
|
1.705
|
0.0989
|
0.311
|
| Metro_vs_SMC |
0
|
5.972
|
1.72e-06
|
1.090
|
| Metro_vs_SMC |
1
|
438.457
|
5.69e-57
|
80.051
|
| Metro_vs_SMC |
2
|
742.119
|
1.34e-63
|
135.492
|
| Metro_vs_SMC |
3
|
505.073
|
9.41e-59
|
92.213
|
| Metro_vs_SMC |
4
|
708.823
|
5.08e-63
|
129.413
|
| Metro_vs_SMC |
5
|
945.358
|
1.2e-66
|
172.598
|
| DEMetro_Z_vs_SMC |
0
|
8.827
|
1.03e-09
|
1.612
|
| DEMetro_Z_vs_SMC |
1
|
16.595
|
2.41e-16
|
3.030
|
| DEMetro_Z_vs_SMC |
2
|
16.465
|
2.97e-16
|
3.006
|
| DEMetro_Z_vs_SMC |
3
|
525.275
|
3.02e-59
|
95.902
|
| DEMetro_Z_vs_SMC |
4
|
780.835
|
3.07e-64
|
142.560
|
| DEMetro_Z_vs_SMC |
5
|
929.588
|
1.95e-66
|
169.719
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
4.434 |
0.080 |
0.044 |
99.283 |
| HMC |
8 |
11.314 |
0.103 |
0.074 |
150.829 |
| HMC |
10 |
17.707 |
0.151 |
0.107 |
164.617 |
| HMC |
12 |
25.421 |
0.156 |
0.112 |
224.612 |
| HMC |
15 |
39.743 |
0.219 |
0.168 |
235.868 |
| HMC |
18 |
57.262 |
0.273 |
0.180 |
316.837 |
| SMC |
5 |
0.074 |
0.080 |
0.044 |
-0.131 |
| SMC |
8 |
0.122 |
0.103 |
0.074 |
0.253 |
| SMC |
10 |
0.136 |
0.151 |
0.107 |
-0.148 |
| SMC |
12 |
0.156 |
0.156 |
0.112 |
-0.003 |
| SMC |
15 |
0.191 |
0.219 |
0.168 |
-0.171 |
| SMC |
18 |
0.208 |
0.273 |
0.180 |
-0.359 |
| Metro |
5 |
1.620 |
0.080 |
0.044 |
35.112 |
| Metro |
8 |
11.320 |
0.103 |
0.074 |
150.911 |
| Metro |
10 |
17.692 |
0.151 |
0.107 |
164.485 |
| Metro |
12 |
25.430 |
0.156 |
0.112 |
224.697 |
| Metro |
15 |
39.752 |
0.219 |
0.168 |
235.918 |
| Metro |
18 |
57.262 |
0.273 |
0.180 |
316.841 |
| DEMetro_Z |
5 |
3.162 |
0.080 |
0.044 |
70.270 |
| DEMetro_Z |
8 |
10.222 |
0.103 |
0.074 |
136.131 |
| DEMetro_Z |
10 |
15.975 |
0.151 |
0.107 |
148.377 |
| DEMetro_Z |
12 |
25.420 |
0.156 |
0.112 |
224.606 |
| DEMetro_Z |
15 |
39.727 |
0.219 |
0.168 |
235.774 |
| DEMetro_Z |
18 |
57.250 |
0.273 |
0.180 |
316.770 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
66.491 |
7.93e-34 |
115.359 |
| HMC |
8 |
75.356 |
2.56e-36 |
83.801 |
| HMC |
10 |
82.943 |
1.49e-38 |
72.939 |
| HMC |
12 |
74.379 |
2.44e-37 |
62.082 |
| HMC |
15 |
70.481 |
2.83e-35 |
83.012 |
| HMC |
18 |
64.341 |
3.85e-34 |
73.946 |
| SMC |
5 |
0.741 |
0.462 |
0.225 |
| SMC |
8 |
-0.457 |
0.649 |
-0.111 |
| SMC |
10 |
-0.036 |
0.971 |
-0.008 |
| SMC |
12 |
-1.046 |
0.301 |
-0.232 |
| SMC |
15 |
1.128 |
0.264 |
0.300 |
| SMC |
18 |
-1.091 |
0.28 |
-0.267 |
| Metro |
5 |
8.403 |
2.89e-09 |
58.550 |
| Metro |
8 |
75.370 |
2.96e-36 |
85.674 |
| Metro |
10 |
69.685 |
1.72e-35 |
72.584 |
| Metro |
12 |
83.303 |
1.8e-39 |
63.630 |
| Metro |
15 |
65.150 |
4.15e-34 |
81.155 |
| Metro |
18 |
67.841 |
5.48e-35 |
74.001 |
| DEMetro_Z |
5 |
9.649 |
1.46e-10 |
85.290 |
| DEMetro_Z |
8 |
16.881 |
1.43e-16 |
77.330 |
| DEMetro_Z |
10 |
17.317 |
7.04e-17 |
65.323 |
| DEMetro_Z |
12 |
94.055 |
4.83e-42 |
64.755 |
| DEMetro_Z |
15 |
77.724 |
7.62e-37 |
83.351 |
| DEMetro_Z |
18 |
78.783 |
1.76e-37 |
74.957 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-2.433
|
0.0214
|
-0.444
|
| Metro_vs_DEMetro_Z |
1
|
1.659
|
0.108
|
0.303
|
| Metro_vs_DEMetro_Z |
2
|
1.665
|
0.107
|
0.304
|
| Metro_vs_DEMetro_Z |
3
|
-1.192
|
0.243
|
-0.218
|
| Metro_vs_DEMetro_Z |
4
|
-1.425
|
0.165
|
-0.260
|
| Metro_vs_DEMetro_Z |
5
|
-0.621
|
0.539
|
-0.113
|
| DEMetro_Z_vs_SMC |
0
|
9.628
|
1.55e-10
|
1.758
|
| DEMetro_Z_vs_SMC |
1
|
16.882
|
1.53e-16
|
3.082
|
| DEMetro_Z_vs_SMC |
2
|
17.296
|
8.08e-17
|
3.158
|
| DEMetro_Z_vs_SMC |
3
|
95.573
|
8.37e-38
|
17.449
|
| DEMetro_Z_vs_SMC |
4
|
77.591
|
3.45e-35
|
14.166
|
| DEMetro_Z_vs_SMC |
5
|
81.736
|
7.68e-36
|
14.923
|
| HMC_vs_DEMetro_Z |
0
|
3.491
|
0.00156
|
0.637
|
| HMC_vs_DEMetro_Z |
1
|
1.325
|
0.196
|
0.242
|
| HMC_vs_DEMetro_Z |
2
|
1.943
|
0.0618
|
0.355
|
| HMC_vs_DEMetro_Z |
3
|
-2.604
|
0.0144
|
-0.475
|
| HMC_vs_DEMetro_Z |
4
|
-0.197
|
0.846
|
-0.036
|
| HMC_vs_DEMetro_Z |
5
|
-0.671
|
0.507
|
-0.123
|
| HMC_vs_Metro |
0
|
7.999
|
8.03e-09
|
1.460
|
| HMC_vs_Metro |
1
|
-1.423
|
0.165
|
-0.260
|
| HMC_vs_Metro |
2
|
0.247
|
0.807
|
0.045
|
| HMC_vs_Metro |
3
|
-1.572
|
0.127
|
-0.287
|
| HMC_vs_Metro |
4
|
0.998
|
0.327
|
0.182
|
| HMC_vs_Metro |
5
|
-0.033
|
0.974
|
-0.006
|
| HMC_vs_SMC |
0
|
66.973
|
2.41e-33
|
12.228
|
| HMC_vs_SMC |
1
|
80.571
|
1.16e-35
|
14.710
|
| HMC_vs_SMC |
2
|
82.193
|
6.54e-36
|
15.006
|
| HMC_vs_SMC |
3
|
74.650
|
1.05e-34
|
13.629
|
| HMC_vs_SMC |
4
|
71.195
|
4.13e-34
|
12.998
|
| HMC_vs_SMC |
5
|
66.553
|
2.89e-33
|
12.151
|
| Metro_vs_SMC |
0
|
8.295
|
3.82e-09
|
1.514
|
| Metro_vs_SMC |
1
|
75.635
|
7.21e-35
|
13.809
|
| Metro_vs_SMC |
2
|
72.156
|
2.81e-34
|
13.174
|
| Metro_vs_SMC |
3
|
86.406
|
1.54e-36
|
15.775
|
| Metro_vs_SMC |
4
|
64.597
|
6.81e-33
|
11.794
|
| Metro_vs_SMC |
5
|
66.468
|
2.99e-33
|
12.135
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
1.584 |
0.048 |
0.013 |
115.359 |
| HMC |
8 |
2.514 |
0.065 |
0.029 |
83.801 |
| HMC |
10 |
3.222 |
0.080 |
0.043 |
72.939 |
| HMC |
12 |
3.756 |
0.093 |
0.059 |
62.082 |
| HMC |
15 |
4.839 |
0.092 |
0.057 |
83.012 |
| HMC |
18 |
5.719 |
0.136 |
0.075 |
73.946 |
| SMC |
5 |
0.051 |
0.048 |
0.013 |
0.225 |
| SMC |
8 |
0.062 |
0.065 |
0.029 |
-0.111 |
| SMC |
10 |
0.079 |
0.080 |
0.043 |
-0.008 |
| SMC |
12 |
0.079 |
0.093 |
0.059 |
-0.232 |
| SMC |
15 |
0.109 |
0.092 |
0.057 |
0.300 |
| SMC |
18 |
0.116 |
0.136 |
0.075 |
-0.267 |
| Metro |
5 |
0.827 |
0.048 |
0.013 |
58.550 |
| Metro |
8 |
2.569 |
0.065 |
0.029 |
85.674 |
| Metro |
10 |
3.206 |
0.080 |
0.043 |
72.584 |
| Metro |
12 |
3.848 |
0.093 |
0.059 |
63.630 |
| Metro |
15 |
4.732 |
0.092 |
0.057 |
81.155 |
| Metro |
18 |
5.723 |
0.136 |
0.075 |
74.001 |
| DEMetro_Z |
5 |
1.183 |
0.048 |
0.013 |
85.290 |
| DEMetro_Z |
8 |
2.325 |
0.065 |
0.029 |
77.330 |
| DEMetro_Z |
10 |
2.894 |
0.080 |
0.043 |
65.323 |
| DEMetro_Z |
12 |
3.914 |
0.093 |
0.059 |
64.755 |
| DEMetro_Z |
15 |
4.858 |
0.092 |
0.057 |
83.351 |
| DEMetro_Z |
18 |
5.795 |
0.136 |
0.075 |
74.957 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
195.023 |
1.07e-53 |
123.600 |
| HMC |
8 |
162.489 |
5.88e-54 |
86.344 |
| HMC |
10 |
139.463 |
5.65e-51 |
76.356 |
| HMC |
12 |
141.437 |
1e-52 |
71.656 |
| HMC |
15 |
145.753 |
3.68e-51 |
82.103 |
| HMC |
18 |
165.601 |
3.81e-57 |
77.823 |
| SMC |
5 |
1.009 |
0.318 |
0.306 |
| SMC |
8 |
-0.601 |
0.551 |
-0.139 |
| SMC |
10 |
-0.190 |
0.85 |
-0.043 |
| SMC |
12 |
-1.188 |
0.24 |
-0.269 |
| SMC |
15 |
1.118 |
0.268 |
0.312 |
| SMC |
18 |
-1.763 |
0.0836 |
-0.403 |
| Metro |
5 |
8.234 |
4.4e-09 |
57.461 |
| Metro |
8 |
198.827 |
3.01e-63 |
84.966 |
| Metro |
10 |
157.182 |
1.99e-55 |
76.340 |
| Metro |
12 |
151.266 |
3.98e-55 |
72.464 |
| Metro |
15 |
149.768 |
5.15e-52 |
82.339 |
| Metro |
18 |
188.248 |
1.48e-63 |
77.583 |
| DEMetro_Z |
5 |
9.469 |
2.22e-10 |
88.887 |
| DEMetro_Z |
8 |
17.049 |
1.1e-16 |
78.485 |
| DEMetro_Z |
10 |
17.500 |
5.37e-17 |
69.053 |
| DEMetro_Z |
12 |
158.934 |
1.18e-57 |
71.515 |
| DEMetro_Z |
15 |
143.957 |
6.06e-51 |
81.210 |
| DEMetro_Z |
18 |
150.589 |
2.36e-53 |
77.688 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
9.445
|
2.37e-10
|
1.724
|
| DEMetro_Z_vs_SMC |
1
|
17.111
|
1.07e-16
|
3.124
|
| DEMetro_Z_vs_SMC |
2
|
17.499
|
5.93e-17
|
3.195
|
| DEMetro_Z_vs_SMC |
3
|
151.526
|
1.35e-43
|
27.665
|
| DEMetro_Z_vs_SMC |
4
|
136.042
|
3.06e-42
|
24.838
|
| DEMetro_Z_vs_SMC |
5
|
159.031
|
3.32e-44
|
29.035
|
| HMC_vs_Metro |
0
|
9.329
|
3.12e-10
|
1.703
|
| HMC_vs_Metro |
1
|
2.433
|
0.0214
|
0.444
|
| HMC_vs_Metro |
2
|
0.021
|
0.983
|
0.004
|
| HMC_vs_Metro |
3
|
-1.734
|
0.0936
|
-0.317
|
| HMC_vs_Metro |
4
|
-0.294
|
0.771
|
-0.054
|
| HMC_vs_Metro |
5
|
0.441
|
0.663
|
0.080
|
| Metro_vs_DEMetro_Z |
0
|
-2.727
|
0.0107
|
-0.498
|
| Metro_vs_DEMetro_Z |
1
|
1.405
|
0.171
|
0.256
|
| Metro_vs_DEMetro_Z |
2
|
1.816
|
0.0797
|
0.332
|
| Metro_vs_DEMetro_Z |
3
|
1.918
|
0.0651
|
0.350
|
| Metro_vs_DEMetro_Z |
4
|
1.696
|
0.101
|
0.310
|
| Metro_vs_DEMetro_Z |
5
|
-0.187
|
0.853
|
-0.034
|
| HMC_vs_SMC |
0
|
197.548
|
6.2e-47
|
36.067
|
| HMC_vs_SMC |
1
|
163.821
|
1.41e-44
|
29.909
|
| HMC_vs_SMC |
2
|
142.773
|
7.56e-43
|
26.067
|
| HMC_vs_SMC |
3
|
145.005
|
4.82e-43
|
26.474
|
| HMC_vs_SMC |
4
|
155.965
|
5.84e-44
|
28.475
|
| HMC_vs_SMC |
5
|
158.076
|
3.96e-44
|
28.861
|
| Metro_vs_SMC |
0
|
8.132
|
5.74e-09
|
1.485
|
| Metro_vs_SMC |
1
|
181.489
|
7.24e-46
|
33.135
|
| Metro_vs_SMC |
2
|
165.968
|
9.65e-45
|
30.301
|
| Metro_vs_SMC |
3
|
162.638
|
1.74e-44
|
29.693
|
| Metro_vs_SMC |
4
|
137.560
|
2.22e-42
|
25.115
|
| Metro_vs_SMC |
5
|
210.566
|
9.76e-48
|
38.444
|
| HMC_vs_DEMetro_Z |
0
|
3.750
|
0.000786
|
0.685
|
| HMC_vs_DEMetro_Z |
1
|
1.696
|
0.101
|
0.310
|
| HMC_vs_DEMetro_Z |
2
|
1.885
|
0.0695
|
0.344
|
| HMC_vs_DEMetro_Z |
3
|
0.262
|
0.795
|
0.048
|
| HMC_vs_DEMetro_Z |
4
|
1.434
|
0.162
|
0.262
|
| HMC_vs_DEMetro_Z |
5
|
0.183
|
0.856
|
0.033
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.557 |
0.012 |
0.004 |
123.600 |
| HMC |
8 |
0.622 |
0.012 |
0.007 |
86.344 |
| HMC |
10 |
0.622 |
0.012 |
0.008 |
76.356 |
| HMC |
12 |
0.621 |
0.012 |
0.008 |
71.656 |
| HMC |
15 |
0.626 |
0.010 |
0.008 |
82.103 |
| HMC |
18 |
0.627 |
0.012 |
0.008 |
77.823 |
| SMC |
5 |
0.014 |
0.012 |
0.004 |
0.306 |
| SMC |
8 |
0.011 |
0.012 |
0.007 |
-0.139 |
| SMC |
10 |
0.012 |
0.012 |
0.008 |
-0.043 |
| SMC |
12 |
0.010 |
0.012 |
0.008 |
-0.269 |
| SMC |
15 |
0.012 |
0.010 |
0.008 |
0.312 |
| SMC |
18 |
0.009 |
0.012 |
0.008 |
-0.403 |
| Metro |
5 |
0.266 |
0.012 |
0.004 |
57.461 |
| Metro |
8 |
0.613 |
0.012 |
0.007 |
84.966 |
| Metro |
10 |
0.622 |
0.012 |
0.008 |
76.340 |
| Metro |
12 |
0.628 |
0.012 |
0.008 |
72.464 |
| Metro |
15 |
0.628 |
0.010 |
0.008 |
82.339 |
| Metro |
18 |
0.625 |
0.012 |
0.008 |
77.583 |
| DEMetro_Z |
5 |
0.404 |
0.012 |
0.004 |
88.887 |
| DEMetro_Z |
8 |
0.567 |
0.012 |
0.007 |
78.485 |
| DEMetro_Z |
10 |
0.564 |
0.012 |
0.008 |
69.053 |
| DEMetro_Z |
12 |
0.620 |
0.012 |
0.008 |
71.515 |
| DEMetro_Z |
15 |
0.620 |
0.010 |
0.008 |
81.210 |
| DEMetro_Z |
18 |
0.626 |
0.012 |
0.008 |
77.688 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
Mode Transitions (scatter)
KDE + Init Plots
Trace Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Varying_Mode_Distance_with_heavy_Tails
(Mixture,
mm,
30 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
3.555 |
0.000772 |
1.001 |
| HMC |
8 |
5.003 |
1.85e-05 |
3.645 |
| HMC |
10 |
4.679 |
4.8e-05 |
3.463 |
| HMC |
12 |
6.005 |
1.22e-06 |
6.084 |
| HMC |
15 |
6.383 |
4.82e-07 |
9.031 |
| HMC |
18 |
5.733 |
2.78e-06 |
6.612 |
| SMC |
5 |
4.620 |
3.74e-05 |
1.985 |
| SMC |
8 |
5.068 |
1.69e-05 |
4.533 |
| SMC |
10 |
5.550 |
3.55e-06 |
3.863 |
| SMC |
12 |
5.170 |
1.06e-05 |
3.425 |
| SMC |
15 |
6.345 |
4.39e-07 |
5.855 |
| SMC |
18 |
3.912 |
0.000481 |
4.950 |
| Metro |
5 |
4.692 |
3.96e-05 |
2.698 |
| Metro |
8 |
5.270 |
7.08e-06 |
3.122 |
| Metro |
10 |
3.066 |
0.00384 |
1.338 |
| Metro |
12 |
3.014 |
0.00511 |
3.032 |
| Metro |
15 |
3.980 |
0.000387 |
4.054 |
| Metro |
18 |
5.745 |
1.85e-06 |
3.718 |
| DEMetro_Z |
5 |
5.776 |
1.27e-06 |
3.017 |
| DEMetro_Z |
8 |
6.173 |
8.26e-07 |
7.631 |
| DEMetro_Z |
10 |
5.470 |
5.23e-06 |
4.758 |
| DEMetro_Z |
12 |
5.240 |
1.21e-05 |
8.309 |
| DEMetro_Z |
15 |
6.968 |
1.08e-07 |
15.121 |
| DEMetro_Z |
18 |
7.721 |
1.5e-08 |
18.256 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-4.271
|
0.000191
|
-0.780
|
| HMC_vs_DEMetro_Z |
1
|
-3.285
|
0.00267
|
-0.600
|
| HMC_vs_DEMetro_Z |
2
|
-1.184
|
0.246
|
-0.216
|
| HMC_vs_DEMetro_Z |
3
|
-1.031
|
0.311
|
-0.188
|
| HMC_vs_DEMetro_Z |
4
|
-2.535
|
0.0169
|
-0.463
|
| HMC_vs_DEMetro_Z |
5
|
-4.325
|
0.000164
|
-0.790
|
| Metro_vs_SMC |
0
|
1.095
|
0.283
|
0.200
|
| Metro_vs_SMC |
1
|
-1.388
|
0.176
|
-0.253
|
| Metro_vs_SMC |
2
|
-3.243
|
0.00297
|
-0.592
|
| Metro_vs_SMC |
3
|
-0.315
|
0.755
|
-0.058
|
| Metro_vs_SMC |
4
|
-1.222
|
0.232
|
-0.223
|
| Metro_vs_SMC |
5
|
-0.903
|
0.374
|
-0.165
|
| Metro_vs_DEMetro_Z |
0
|
-0.375
|
0.711
|
-0.068
|
| Metro_vs_DEMetro_Z |
1
|
-3.237
|
0.00302
|
-0.591
|
| Metro_vs_DEMetro_Z |
2
|
-3.770
|
0.000744
|
-0.688
|
| Metro_vs_DEMetro_Z |
3
|
-2.694
|
0.0116
|
-0.492
|
| Metro_vs_DEMetro_Z |
4
|
-4.883
|
3.51e-05
|
-0.892
|
| Metro_vs_DEMetro_Z |
5
|
-6.199
|
9.24e-07
|
-1.132
|
| HMC_vs_Metro |
0
|
-2.747
|
0.0102
|
-0.502
|
| HMC_vs_Metro |
1
|
0.591
|
0.559
|
0.108
|
| HMC_vs_Metro |
2
|
2.764
|
0.00981
|
0.505
|
| HMC_vs_Metro |
3
|
2.220
|
0.0344
|
0.405
|
| HMC_vs_Metro |
4
|
2.697
|
0.0115
|
0.492
|
| HMC_vs_Metro |
5
|
2.145
|
0.0405
|
0.392
|
| HMC_vs_SMC |
0
|
-2.203
|
0.0357
|
-0.402
|
| HMC_vs_SMC |
1
|
-0.742
|
0.464
|
-0.135
|
| HMC_vs_SMC |
2
|
-0.427
|
0.672
|
-0.078
|
| HMC_vs_SMC |
3
|
2.348
|
0.0259
|
0.429
|
| HMC_vs_SMC |
4
|
2.005
|
0.0544
|
0.366
|
| HMC_vs_SMC |
5
|
1.596
|
0.121
|
0.291
|
| DEMetro_Z_vs_SMC |
0
|
1.606
|
0.119
|
0.293
|
| DEMetro_Z_vs_SMC |
1
|
1.975
|
0.0579
|
0.361
|
| DEMetro_Z_vs_SMC |
2
|
0.912
|
0.369
|
0.167
|
| DEMetro_Z_vs_SMC |
3
|
2.792
|
0.00918
|
0.510
|
| DEMetro_Z_vs_SMC |
4
|
4.091
|
0.000313
|
0.747
|
| DEMetro_Z_vs_SMC |
5
|
5.248
|
1.27e-05
|
0.958
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.094 |
0.059 |
0.035 |
1.001 |
| HMC |
8 |
0.188 |
0.067 |
0.033 |
3.645 |
| HMC |
10 |
0.323 |
0.102 |
0.064 |
3.463 |
| HMC |
12 |
0.540 |
0.098 |
0.073 |
6.084 |
| HMC |
15 |
0.796 |
0.123 |
0.074 |
9.031 |
| HMC |
18 |
0.805 |
0.115 |
0.104 |
6.612 |
| SMC |
5 |
0.129 |
0.059 |
0.035 |
1.985 |
| SMC |
8 |
0.218 |
0.067 |
0.033 |
4.533 |
| SMC |
10 |
0.349 |
0.102 |
0.064 |
3.863 |
| SMC |
12 |
0.347 |
0.098 |
0.073 |
3.425 |
| SMC |
15 |
0.559 |
0.123 |
0.074 |
5.855 |
| SMC |
18 |
0.631 |
0.115 |
0.104 |
4.950 |
| Metro |
5 |
0.154 |
0.059 |
0.035 |
2.698 |
| Metro |
8 |
0.171 |
0.067 |
0.033 |
3.122 |
| Metro |
10 |
0.187 |
0.102 |
0.064 |
1.338 |
| Metro |
12 |
0.318 |
0.098 |
0.073 |
3.032 |
| Metro |
15 |
0.425 |
0.123 |
0.074 |
4.054 |
| Metro |
18 |
0.503 |
0.115 |
0.104 |
3.718 |
| DEMetro_Z |
5 |
0.165 |
0.059 |
0.035 |
3.017 |
| DEMetro_Z |
8 |
0.321 |
0.067 |
0.033 |
7.631 |
| DEMetro_Z |
10 |
0.406 |
0.102 |
0.064 |
4.758 |
| DEMetro_Z |
12 |
0.701 |
0.098 |
0.073 |
8.309 |
| DEMetro_Z |
15 |
1.249 |
0.123 |
0.074 |
15.121 |
| DEMetro_Z |
18 |
2.020 |
0.115 |
0.104 |
18.256 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
-1.411 |
0.169 |
-0.259 |
| HMC |
8 |
-0.170 |
0.866 |
-0.039 |
| HMC |
10 |
-1.580 |
0.125 |
-0.290 |
| HMC |
12 |
0.372 |
0.711 |
0.118 |
| HMC |
15 |
0.729 |
0.471 |
0.605 |
| HMC |
18 |
-0.982 |
0.334 |
-0.179 |
| SMC |
5 |
-1.233 |
0.227 |
-0.226 |
| SMC |
8 |
-0.652 |
0.519 |
-0.122 |
| SMC |
10 |
-1.713 |
0.0971 |
-0.314 |
| SMC |
12 |
-0.587 |
0.561 |
-0.115 |
| SMC |
15 |
-1.694 |
0.1 |
-0.316 |
| SMC |
18 |
-0.970 |
0.34 |
-0.177 |
| Metro |
5 |
-1.237 |
0.226 |
-0.227 |
| Metro |
8 |
-1.374 |
0.179 |
-0.256 |
| Metro |
10 |
-1.454 |
0.156 |
-0.268 |
| Metro |
12 |
0.817 |
0.42 |
0.751 |
| Metro |
15 |
-1.320 |
0.196 |
-0.249 |
| Metro |
18 |
-0.925 |
0.363 |
-0.169 |
| DEMetro_Z |
5 |
-1.182 |
0.246 |
-0.218 |
| DEMetro_Z |
8 |
-1.029 |
0.311 |
-0.195 |
| DEMetro_Z |
10 |
-1.383 |
0.177 |
-0.255 |
| DEMetro_Z |
12 |
-0.188 |
0.852 |
-0.037 |
| DEMetro_Z |
15 |
-0.209 |
0.836 |
-0.042 |
| DEMetro_Z |
18 |
-0.860 |
0.397 |
-0.157 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
-1.541
|
0.134
|
-0.281
|
| HMC_vs_SMC |
1
|
0.522
|
0.606
|
0.095
|
| HMC_vs_SMC |
2
|
1.675
|
0.105
|
0.306
|
| HMC_vs_SMC |
3
|
0.959
|
0.346
|
0.175
|
| HMC_vs_SMC |
4
|
1.151
|
0.259
|
0.210
|
| HMC_vs_SMC |
5
|
-0.605
|
0.55
|
-0.111
|
| Metro_vs_DEMetro_Z |
0
|
-0.409
|
0.686
|
-0.075
|
| Metro_vs_DEMetro_Z |
1
|
-1.267
|
0.215
|
-0.231
|
| Metro_vs_DEMetro_Z |
2
|
-0.647
|
0.523
|
-0.118
|
| Metro_vs_DEMetro_Z |
3
|
0.871
|
0.391
|
0.159
|
| Metro_vs_DEMetro_Z |
4
|
-2.631
|
0.0135
|
-0.480
|
| Metro_vs_DEMetro_Z |
5
|
-1.817
|
0.0796
|
-0.332
|
| HMC_vs_Metro |
0
|
-1.799
|
0.0824
|
-0.329
|
| HMC_vs_Metro |
1
|
1.440
|
0.16
|
0.263
|
| HMC_vs_Metro |
2
|
-1.291
|
0.207
|
-0.236
|
| HMC_vs_Metro |
3
|
-0.668
|
0.509
|
-0.122
|
| HMC_vs_Metro |
4
|
1.048
|
0.303
|
0.191
|
| HMC_vs_Metro |
5
|
-1.024
|
0.314
|
-0.187
|
| HMC_vs_DEMetro_Z |
0
|
-2.245
|
0.0326
|
-0.410
|
| HMC_vs_DEMetro_Z |
1
|
0.984
|
0.333
|
0.180
|
| HMC_vs_DEMetro_Z |
2
|
-2.115
|
0.0432
|
-0.386
|
| HMC_vs_DEMetro_Z |
3
|
0.609
|
0.547
|
0.111
|
| HMC_vs_DEMetro_Z |
4
|
0.782
|
0.44
|
0.143
|
| HMC_vs_DEMetro_Z |
5
|
-3.890
|
0.000539
|
-0.710
|
| Metro_vs_SMC |
0
|
-0.038
|
0.97
|
-0.007
|
| Metro_vs_SMC |
1
|
-2.336
|
0.0266
|
-0.427
|
| Metro_vs_SMC |
2
|
2.802
|
0.00896
|
0.512
|
| Metro_vs_SMC |
3
|
0.957
|
0.347
|
0.175
|
| Metro_vs_SMC |
4
|
1.170
|
0.252
|
0.214
|
| Metro_vs_SMC |
5
|
1.096
|
0.282
|
0.200
|
| DEMetro_Z_vs_SMC |
0
|
0.314
|
0.755
|
0.057
|
| DEMetro_Z_vs_SMC |
1
|
-1.136
|
0.265
|
-0.207
|
| DEMetro_Z_vs_SMC |
2
|
3.818
|
0.000654
|
0.697
|
| DEMetro_Z_vs_SMC |
3
|
1.363
|
0.184
|
0.249
|
| DEMetro_Z_vs_SMC |
4
|
2.946
|
0.00628
|
0.538
|
| DEMetro_Z_vs_SMC |
5
|
4.951
|
2.9e-05
|
0.904
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
4.008 |
12.658 |
33.375 |
-0.259 |
| HMC |
8 |
8.338 |
9.038 |
17.720 |
-0.039 |
| HMC |
10 |
4.768 |
15.206 |
35.981 |
-0.290 |
| HMC |
12 |
7.063 |
5.828 |
10.481 |
0.118 |
| HMC |
15 |
14.271 |
7.481 |
11.222 |
0.605 |
| HMC |
18 |
5.745 |
72.410 |
371.981 |
-0.179 |
| SMC |
5 |
5.103 |
12.658 |
33.375 |
-0.226 |
| SMC |
8 |
6.877 |
9.038 |
17.720 |
-0.122 |
| SMC |
10 |
3.909 |
15.206 |
35.981 |
-0.314 |
| SMC |
12 |
4.621 |
5.828 |
10.481 |
-0.115 |
| SMC |
15 |
3.932 |
7.481 |
11.222 |
-0.316 |
| SMC |
18 |
6.549 |
72.410 |
371.981 |
-0.177 |
| Metro |
5 |
5.073 |
12.658 |
33.375 |
-0.227 |
| Metro |
8 |
4.498 |
9.038 |
17.720 |
-0.256 |
| Metro |
10 |
5.575 |
15.206 |
35.981 |
-0.268 |
| Metro |
12 |
13.705 |
5.828 |
10.481 |
0.751 |
| Metro |
15 |
4.689 |
7.481 |
11.222 |
-0.249 |
| Metro |
18 |
9.515 |
72.410 |
371.981 |
-0.169 |
| DEMetro_Z |
5 |
5.392 |
12.658 |
33.375 |
-0.218 |
| DEMetro_Z |
8 |
5.582 |
9.038 |
17.720 |
-0.195 |
| DEMetro_Z |
10 |
6.042 |
15.206 |
35.981 |
-0.255 |
| DEMetro_Z |
12 |
5.436 |
5.828 |
10.481 |
-0.037 |
| DEMetro_Z |
15 |
7.013 |
7.481 |
11.222 |
-0.042 |
| DEMetro_Z |
18 |
13.948 |
72.410 |
371.981 |
-0.157 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
3.550 |
0.000783 |
0.993 |
| HMC |
8 |
5.146 |
1.24e-05 |
3.858 |
| HMC |
10 |
5.560 |
3.44e-06 |
3.862 |
| HMC |
12 |
6.189 |
7.94e-07 |
7.755 |
| HMC |
15 |
6.394 |
4.76e-07 |
9.725 |
| HMC |
18 |
6.022 |
1.1e-06 |
5.519 |
| SMC |
5 |
7.558 |
4.45e-09 |
3.743 |
| SMC |
8 |
13.396 |
3.72e-15 |
8.530 |
| SMC |
10 |
8.664 |
4.37e-10 |
5.788 |
| SMC |
12 |
10.377 |
4.66e-12 |
6.770 |
| SMC |
15 |
9.688 |
4.88e-11 |
7.957 |
| SMC |
18 |
5.802 |
2.11e-06 |
5.538 |
| Metro |
5 |
6.325 |
1e-07 |
2.382 |
| Metro |
8 |
6.736 |
4.39e-08 |
3.033 |
| Metro |
10 |
4.681 |
3.23e-05 |
2.092 |
| Metro |
12 |
4.142 |
0.00025 |
4.611 |
| Metro |
15 |
4.894 |
2.94e-05 |
5.012 |
| Metro |
18 |
5.449 |
4.72e-06 |
3.719 |
| DEMetro_Z |
5 |
9.367 |
2.49e-12 |
3.359 |
| DEMetro_Z |
8 |
7.539 |
1.78e-08 |
7.994 |
| DEMetro_Z |
10 |
7.232 |
3.52e-08 |
6.419 |
| DEMetro_Z |
12 |
6.097 |
1.12e-06 |
10.752 |
| DEMetro_Z |
15 |
7.609 |
1.97e-08 |
16.195 |
| DEMetro_Z |
18 |
7.854 |
1.04e-08 |
15.914 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-2.086
|
0.0459
|
-0.381
|
| Metro_vs_DEMetro_Z |
1
|
-4.250
|
0.000202
|
-0.776
|
| Metro_vs_DEMetro_Z |
2
|
-4.727
|
5.41e-05
|
-0.863
|
| Metro_vs_DEMetro_Z |
3
|
-2.864
|
0.0077
|
-0.523
|
| Metro_vs_DEMetro_Z |
4
|
-5.036
|
2.29e-05
|
-0.920
|
| Metro_vs_DEMetro_Z |
5
|
-6.479
|
4.32e-07
|
-1.183
|
| DEMetro_Z_vs_SMC |
0
|
-0.743
|
0.463
|
-0.136
|
| DEMetro_Z_vs_SMC |
1
|
-0.407
|
0.687
|
-0.074
|
| DEMetro_Z_vs_SMC |
2
|
0.698
|
0.491
|
0.127
|
| DEMetro_Z_vs_SMC |
3
|
2.133
|
0.0415
|
0.389
|
| DEMetro_Z_vs_SMC |
4
|
3.714
|
0.000864
|
0.678
|
| DEMetro_Z_vs_SMC |
5
|
4.833
|
4.04e-05
|
0.882
|
| HMC_vs_DEMetro_Z |
0
|
-7.481
|
3.03e-08
|
-1.366
|
| HMC_vs_DEMetro_Z |
1
|
-4.089
|
0.000314
|
-0.747
|
| HMC_vs_DEMetro_Z |
2
|
-2.489
|
0.0188
|
-0.454
|
| HMC_vs_DEMetro_Z |
3
|
-1.207
|
0.237
|
-0.220
|
| HMC_vs_DEMetro_Z |
4
|
-2.672
|
0.0123
|
-0.488
|
| HMC_vs_DEMetro_Z |
5
|
-4.609
|
7.51e-05
|
-0.841
|
| HMC_vs_Metro |
0
|
-3.534
|
0.00139
|
-0.645
|
| HMC_vs_Metro |
1
|
0.928
|
0.361
|
0.169
|
| HMC_vs_Metro |
2
|
2.353
|
0.0256
|
0.430
|
| HMC_vs_Metro |
3
|
1.924
|
0.0642
|
0.351
|
| HMC_vs_Metro |
4
|
2.402
|
0.0229
|
0.439
|
| HMC_vs_Metro |
5
|
1.559
|
0.13
|
0.285
|
| HMC_vs_SMC |
0
|
-5.976
|
1.7e-06
|
-1.091
|
| HMC_vs_SMC |
1
|
-4.347
|
0.000155
|
-0.794
|
| HMC_vs_SMC |
2
|
-2.194
|
0.0364
|
-0.401
|
| HMC_vs_SMC |
3
|
0.684
|
0.5
|
0.125
|
| HMC_vs_SMC |
4
|
1.161
|
0.255
|
0.212
|
| HMC_vs_SMC |
5
|
-0.024
|
0.981
|
-0.004
|
| Metro_vs_SMC |
0
|
-2.641
|
0.0132
|
-0.482
|
| Metro_vs_SMC |
1
|
-6.880
|
1.47e-07
|
-1.256
|
| Metro_vs_SMC |
2
|
-4.695
|
5.92e-05
|
-0.857
|
| Metro_vs_SMC |
3
|
-1.632
|
0.113
|
-0.298
|
| Metro_vs_SMC |
4
|
-2.089
|
0.0456
|
-0.381
|
| Metro_vs_SMC |
5
|
-1.647
|
0.11
|
-0.301
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.180 |
0.131 |
0.049 |
0.993 |
| HMC |
8 |
0.293 |
0.144 |
0.039 |
3.858 |
| HMC |
10 |
0.381 |
0.176 |
0.053 |
3.862 |
| HMC |
12 |
0.587 |
0.162 |
0.055 |
7.755 |
| HMC |
15 |
0.817 |
0.184 |
0.065 |
9.725 |
| HMC |
18 |
0.808 |
0.192 |
0.112 |
5.519 |
| SMC |
5 |
0.315 |
0.131 |
0.049 |
3.743 |
| SMC |
8 |
0.474 |
0.144 |
0.039 |
8.530 |
| SMC |
10 |
0.483 |
0.176 |
0.053 |
5.788 |
| SMC |
12 |
0.533 |
0.162 |
0.055 |
6.770 |
| SMC |
15 |
0.702 |
0.184 |
0.065 |
7.957 |
| SMC |
18 |
0.811 |
0.192 |
0.112 |
5.538 |
| Metro |
5 |
0.248 |
0.131 |
0.049 |
2.382 |
| Metro |
8 |
0.261 |
0.144 |
0.039 |
3.033 |
| Metro |
10 |
0.287 |
0.176 |
0.053 |
2.092 |
| Metro |
12 |
0.415 |
0.162 |
0.055 |
4.611 |
| Metro |
15 |
0.510 |
0.184 |
0.065 |
5.012 |
| Metro |
18 |
0.607 |
0.192 |
0.112 |
3.719 |
| DEMetro_Z |
5 |
0.296 |
0.131 |
0.049 |
3.359 |
| DEMetro_Z |
8 |
0.453 |
0.144 |
0.039 |
7.994 |
| DEMetro_Z |
10 |
0.516 |
0.176 |
0.053 |
6.419 |
| DEMetro_Z |
12 |
0.751 |
0.162 |
0.055 |
10.752 |
| DEMetro_Z |
15 |
1.238 |
0.184 |
0.065 |
16.195 |
| DEMetro_Z |
18 |
1.970 |
0.192 |
0.112 |
15.914 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
5.068 |
1.03e-05 |
2.413 |
| HMC |
8 |
5.447 |
6.09e-06 |
5.738 |
| HMC |
10 |
5.470 |
5.42e-06 |
5.123 |
| HMC |
12 |
6.131 |
9.47e-07 |
8.031 |
| HMC |
15 |
6.164 |
9.29e-07 |
10.845 |
| HMC |
18 |
5.391 |
8.37e-06 |
16.173 |
| SMC |
5 |
9.518 |
6.82e-11 |
7.483 |
| SMC |
8 |
9.053 |
3.43e-10 |
9.435 |
| SMC |
10 |
6.931 |
8.56e-08 |
6.531 |
| SMC |
12 |
6.590 |
1.95e-07 |
5.296 |
| SMC |
15 |
6.910 |
9.85e-08 |
7.293 |
| SMC |
18 |
4.052 |
0.000344 |
13.094 |
| Metro |
5 |
6.201 |
4.05e-07 |
3.589 |
| Metro |
8 |
6.082 |
6.95e-07 |
4.026 |
| Metro |
10 |
3.944 |
0.000348 |
2.101 |
| Metro |
12 |
5.915 |
9.26e-07 |
3.321 |
| Metro |
15 |
4.464 |
0.000102 |
4.996 |
| Metro |
18 |
6.189 |
8.25e-07 |
8.712 |
| DEMetro_Z |
5 |
9.703 |
2.98e-11 |
6.624 |
| DEMetro_Z |
8 |
6.635 |
2.54e-07 |
11.388 |
| DEMetro_Z |
10 |
6.015 |
1.27e-06 |
7.206 |
| DEMetro_Z |
12 |
5.190 |
1.44e-05 |
11.257 |
| DEMetro_Z |
15 |
6.778 |
1.85e-07 |
18.730 |
| DEMetro_Z |
18 |
7.501 |
2.85e-08 |
48.873 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
-0.873
|
0.39
|
-0.159
|
| DEMetro_Z_vs_SMC |
1
|
0.906
|
0.372
|
0.166
|
| DEMetro_Z_vs_SMC |
2
|
0.513
|
0.612
|
0.094
|
| DEMetro_Z_vs_SMC |
3
|
2.483
|
0.0191
|
0.453
|
| DEMetro_Z_vs_SMC |
4
|
4.005
|
0.000395
|
0.731
|
| DEMetro_Z_vs_SMC |
5
|
5.184
|
1.52e-05
|
0.946
|
| HMC_vs_Metro |
0
|
-1.982
|
0.057
|
-0.362
|
| HMC_vs_Metro |
1
|
1.241
|
0.224
|
0.227
|
| HMC_vs_Metro |
2
|
3.074
|
0.00457
|
0.561
|
| HMC_vs_Metro |
3
|
3.107
|
0.00421
|
0.567
|
| HMC_vs_Metro |
4
|
2.646
|
0.013
|
0.483
|
| HMC_vs_Metro |
5
|
2.216
|
0.0347
|
0.405
|
| Metro_vs_DEMetro_Z |
0
|
-3.560
|
0.0013
|
-0.650
|
| Metro_vs_DEMetro_Z |
1
|
-3.810
|
0.000668
|
-0.696
|
| Metro_vs_DEMetro_Z |
2
|
-4.235
|
0.00021
|
-0.773
|
| Metro_vs_DEMetro_Z |
3
|
-3.497
|
0.00153
|
-0.639
|
| Metro_vs_DEMetro_Z |
4
|
-4.871
|
3.63e-05
|
-0.889
|
| Metro_vs_DEMetro_Z |
5
|
-6.296
|
7.1e-07
|
-1.149
|
| HMC_vs_SMC |
0
|
-5.609
|
4.68e-06
|
-1.024
|
| HMC_vs_SMC |
1
|
-2.362
|
0.0251
|
-0.431
|
| HMC_vs_SMC |
2
|
-1.201
|
0.24
|
-0.219
|
| HMC_vs_SMC |
3
|
1.860
|
0.073
|
0.340
|
| HMC_vs_SMC |
4
|
1.849
|
0.0746
|
0.338
|
| HMC_vs_SMC |
5
|
1.283
|
0.21
|
0.234
|
| Metro_vs_SMC |
0
|
-4.440
|
0.00012
|
-0.811
|
| Metro_vs_SMC |
1
|
-4.570
|
8.37e-05
|
-0.834
|
| Metro_vs_SMC |
2
|
-4.303
|
0.000175
|
-0.786
|
| Metro_vs_SMC |
3
|
-2.024
|
0.0523
|
-0.370
|
| Metro_vs_SMC |
4
|
-1.388
|
0.176
|
-0.253
|
| Metro_vs_SMC |
5
|
-1.271
|
0.214
|
-0.232
|
| HMC_vs_DEMetro_Z |
0
|
-6.436
|
4.85e-07
|
-1.175
|
| HMC_vs_DEMetro_Z |
1
|
-3.069
|
0.00462
|
-0.560
|
| HMC_vs_DEMetro_Z |
2
|
-1.478
|
0.15
|
-0.270
|
| HMC_vs_DEMetro_Z |
3
|
-1.114
|
0.274
|
-0.203
|
| HMC_vs_DEMetro_Z |
4
|
-2.514
|
0.0177
|
-0.459
|
| HMC_vs_DEMetro_Z |
5
|
-4.458
|
0.000114
|
-0.814
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.022 |
0.012 |
0.004 |
2.413 |
| HMC |
8 |
0.034 |
0.011 |
0.004 |
5.738 |
| HMC |
10 |
0.048 |
0.013 |
0.007 |
5.123 |
| HMC |
12 |
0.069 |
0.012 |
0.007 |
8.031 |
| HMC |
15 |
0.085 |
0.012 |
0.007 |
10.845 |
| HMC |
18 |
0.072 |
0.009 |
0.004 |
16.173 |
| SMC |
5 |
0.044 |
0.012 |
0.004 |
7.483 |
| SMC |
8 |
0.049 |
0.011 |
0.004 |
9.435 |
| SMC |
10 |
0.058 |
0.013 |
0.007 |
6.531 |
| SMC |
12 |
0.049 |
0.012 |
0.007 |
5.296 |
| SMC |
15 |
0.061 |
0.012 |
0.007 |
7.293 |
| SMC |
18 |
0.060 |
0.009 |
0.004 |
13.094 |
| Metro |
5 |
0.027 |
0.012 |
0.004 |
3.589 |
| Metro |
8 |
0.027 |
0.011 |
0.004 |
4.026 |
| Metro |
10 |
0.028 |
0.013 |
0.007 |
2.101 |
| Metro |
12 |
0.035 |
0.012 |
0.007 |
3.321 |
| Metro |
15 |
0.045 |
0.012 |
0.007 |
4.996 |
| Metro |
18 |
0.043 |
0.009 |
0.004 |
8.712 |
| DEMetro_Z |
5 |
0.040 |
0.012 |
0.004 |
6.624 |
| DEMetro_Z |
8 |
0.057 |
0.011 |
0.004 |
11.388 |
| DEMetro_Z |
10 |
0.063 |
0.013 |
0.007 |
7.206 |
| DEMetro_Z |
12 |
0.091 |
0.012 |
0.007 |
11.257 |
| DEMetro_Z |
15 |
0.138 |
0.012 |
0.007 |
18.730 |
| DEMetro_Z |
18 |
0.201 |
0.009 |
0.004 |
48.873 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
3.108 |
0.00332 |
1.241 |
| HMC |
8 |
4.156 |
0.000228 |
3.538 |
| HMC |
10 |
5.077 |
1.56e-05 |
4.023 |
| HMC |
12 |
6.226 |
5.79e-07 |
5.275 |
| HMC |
15 |
4.774 |
4.28e-05 |
5.662 |
| HMC |
18 |
7.194 |
4.03e-08 |
6.583 |
| SMC |
5 |
3.135 |
0.0031 |
1.268 |
| SMC |
8 |
4.309 |
0.000149 |
3.811 |
| SMC |
10 |
5.114 |
1.07e-05 |
2.858 |
| SMC |
12 |
5.247 |
8.66e-06 |
3.619 |
| SMC |
15 |
6.221 |
6e-07 |
5.425 |
| SMC |
18 |
4.912 |
2.84e-05 |
5.445 |
| Metro |
5 |
4.929 |
2.28e-05 |
3.541 |
| Metro |
8 |
3.620 |
0.00098 |
2.664 |
| Metro |
10 |
4.140 |
0.000195 |
2.190 |
| Metro |
12 |
3.026 |
0.00497 |
3.217 |
| Metro |
15 |
4.639 |
6.29e-05 |
5.583 |
| Metro |
18 |
4.087 |
0.000303 |
6.339 |
| DEMetro_Z |
5 |
6.151 |
4.2e-07 |
3.320 |
| DEMetro_Z |
8 |
6.850 |
1.11e-07 |
6.750 |
| DEMetro_Z |
10 |
4.364 |
9.02e-05 |
2.035 |
| DEMetro_Z |
12 |
4.220 |
0.000208 |
5.931 |
| DEMetro_Z |
15 |
5.147 |
1.64e-05 |
13.088 |
| DEMetro_Z |
18 |
5.251 |
1.24e-05 |
17.678 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-3.843
|
0.000611
|
-0.702
|
| HMC_vs_DEMetro_Z |
1
|
-2.605
|
0.0143
|
-0.476
|
| HMC_vs_DEMetro_Z |
2
|
2.217
|
0.0346
|
0.405
|
| HMC_vs_DEMetro_Z |
3
|
-0.381
|
0.706
|
-0.070
|
| HMC_vs_DEMetro_Z |
4
|
-2.470
|
0.0196
|
-0.451
|
| HMC_vs_DEMetro_Z |
5
|
-2.864
|
0.00769
|
-0.523
|
| Metro_vs_SMC |
0
|
3.015
|
0.00529
|
0.551
|
| Metro_vs_SMC |
1
|
-0.923
|
0.364
|
-0.169
|
| Metro_vs_SMC |
2
|
-1.203
|
0.239
|
-0.220
|
| Metro_vs_SMC |
3
|
-0.297
|
0.769
|
-0.054
|
| Metro_vs_SMC |
4
|
0.102
|
0.92
|
0.019
|
| Metro_vs_SMC |
5
|
0.477
|
0.637
|
0.087
|
| Metro_vs_DEMetro_Z |
0
|
0.268
|
0.791
|
0.049
|
| Metro_vs_DEMetro_Z |
1
|
-3.233
|
0.00305
|
-0.590
|
| Metro_vs_DEMetro_Z |
2
|
0.223
|
0.825
|
0.041
|
| Metro_vs_DEMetro_Z |
3
|
-1.650
|
0.11
|
-0.301
|
| Metro_vs_DEMetro_Z |
4
|
-2.491
|
0.0187
|
-0.455
|
| Metro_vs_DEMetro_Z |
5
|
-3.619
|
0.00111
|
-0.661
|
| HMC_vs_Metro |
0
|
-2.755
|
0.01
|
-0.503
|
| HMC_vs_Metro |
1
|
0.750
|
0.459
|
0.137
|
| HMC_vs_Metro |
2
|
1.888
|
0.0691
|
0.345
|
| HMC_vs_Metro |
3
|
1.476
|
0.151
|
0.269
|
| HMC_vs_Metro |
4
|
0.041
|
0.967
|
0.008
|
| HMC_vs_Metro |
5
|
0.119
|
0.906
|
0.022
|
| HMC_vs_SMC |
0
|
-0.053
|
0.958
|
-0.010
|
| HMC_vs_SMC |
1
|
-0.204
|
0.84
|
-0.037
|
| HMC_vs_SMC |
2
|
1.106
|
0.278
|
0.202
|
| HMC_vs_SMC |
3
|
1.687
|
0.102
|
0.308
|
| HMC_vs_SMC |
4
|
0.153
|
0.88
|
0.028
|
| HMC_vs_SMC |
5
|
0.783
|
0.44
|
0.143
|
| DEMetro_Z_vs_SMC |
0
|
3.185
|
0.00345
|
0.582
|
| DEMetro_Z_vs_SMC |
1
|
2.265
|
0.0312
|
0.414
|
| DEMetro_Z_vs_SMC |
2
|
-1.260
|
0.218
|
-0.230
|
| DEMetro_Z_vs_SMC |
3
|
1.416
|
0.167
|
0.259
|
| DEMetro_Z_vs_SMC |
4
|
2.956
|
0.00614
|
0.540
|
| DEMetro_Z_vs_SMC |
5
|
3.499
|
0.00153
|
0.639
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.103 |
0.059 |
0.035 |
1.241 |
| HMC |
8 |
0.185 |
0.067 |
0.033 |
3.538 |
| HMC |
10 |
0.359 |
0.102 |
0.064 |
4.023 |
| HMC |
12 |
0.481 |
0.098 |
0.073 |
5.275 |
| HMC |
15 |
0.545 |
0.123 |
0.074 |
5.662 |
| HMC |
18 |
0.802 |
0.115 |
0.104 |
6.583 |
| SMC |
5 |
0.103 |
0.059 |
0.035 |
1.268 |
| SMC |
8 |
0.194 |
0.067 |
0.033 |
3.811 |
| SMC |
10 |
0.284 |
0.102 |
0.064 |
2.858 |
| SMC |
12 |
0.361 |
0.098 |
0.073 |
3.619 |
| SMC |
15 |
0.527 |
0.123 |
0.074 |
5.425 |
| SMC |
18 |
0.683 |
0.115 |
0.104 |
5.445 |
| Metro |
5 |
0.184 |
0.059 |
0.035 |
3.541 |
| Metro |
8 |
0.156 |
0.067 |
0.033 |
2.664 |
| Metro |
10 |
0.242 |
0.102 |
0.064 |
2.190 |
| Metro |
12 |
0.332 |
0.098 |
0.073 |
3.217 |
| Metro |
15 |
0.539 |
0.123 |
0.074 |
5.583 |
| Metro |
18 |
0.776 |
0.115 |
0.104 |
6.339 |
| DEMetro_Z |
5 |
0.176 |
0.059 |
0.035 |
3.320 |
| DEMetro_Z |
8 |
0.292 |
0.067 |
0.033 |
6.750 |
| DEMetro_Z |
10 |
0.232 |
0.102 |
0.064 |
2.035 |
| DEMetro_Z |
12 |
0.528 |
0.098 |
0.073 |
5.931 |
| DEMetro_Z |
15 |
1.098 |
0.123 |
0.074 |
13.088 |
| DEMetro_Z |
18 |
1.959 |
0.115 |
0.104 |
17.678 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
-1.368 |
0.182 |
-0.251 |
| HMC |
8 |
-1.469 |
0.152 |
-0.274 |
| HMC |
10 |
-0.831 |
0.41 |
-0.174 |
| HMC |
12 |
-0.430 |
0.669 |
-0.096 |
| HMC |
15 |
-1.224 |
0.228 |
-0.245 |
| HMC |
18 |
-0.849 |
0.402 |
-0.156 |
| SMC |
5 |
-1.506 |
0.143 |
-0.276 |
| SMC |
8 |
-1.238 |
0.225 |
-0.230 |
| SMC |
10 |
-1.795 |
0.083 |
-0.329 |
| SMC |
12 |
-1.295 |
0.203 |
-0.252 |
| SMC |
15 |
-1.953 |
0.0597 |
-0.365 |
| SMC |
18 |
-0.970 |
0.34 |
-0.177 |
| Metro |
5 |
-0.993 |
0.328 |
-0.190 |
| Metro |
8 |
-1.044 |
0.303 |
-0.208 |
| Metro |
10 |
-1.565 |
0.128 |
-0.287 |
| Metro |
12 |
0.378 |
0.707 |
0.099 |
| Metro |
15 |
0.754 |
0.456 |
0.576 |
| Metro |
18 |
-0.952 |
0.349 |
-0.174 |
| DEMetro_Z |
5 |
-1.300 |
0.204 |
-0.239 |
| DEMetro_Z |
8 |
-1.489 |
0.147 |
-0.276 |
| DEMetro_Z |
10 |
-1.506 |
0.143 |
-0.277 |
| DEMetro_Z |
12 |
0.009 |
0.993 |
0.002 |
| DEMetro_Z |
15 |
-0.264 |
0.793 |
-0.056 |
| DEMetro_Z |
18 |
-0.813 |
0.423 |
-0.149 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
1.824
|
0.0784
|
0.333
|
| HMC_vs_SMC |
1
|
-1.025
|
0.314
|
-0.187
|
| HMC_vs_SMC |
2
|
1.476
|
0.151
|
0.270
|
| HMC_vs_SMC |
3
|
1.357
|
0.185
|
0.248
|
| HMC_vs_SMC |
4
|
1.586
|
0.124
|
0.290
|
| HMC_vs_SMC |
5
|
1.231
|
0.228
|
0.225
|
| Metro_vs_DEMetro_Z |
0
|
0.923
|
0.364
|
0.168
|
| Metro_vs_DEMetro_Z |
1
|
0.819
|
0.419
|
0.150
|
| Metro_vs_DEMetro_Z |
2
|
-1.089
|
0.285
|
-0.199
|
| Metro_vs_DEMetro_Z |
3
|
0.523
|
0.605
|
0.096
|
| Metro_vs_DEMetro_Z |
4
|
0.834
|
0.411
|
0.152
|
| Metro_vs_DEMetro_Z |
5
|
-3.245
|
0.00295
|
-0.593
|
| HMC_vs_Metro |
0
|
-1.114
|
0.274
|
-0.203
|
| HMC_vs_Metro |
1
|
-0.763
|
0.452
|
-0.139
|
| HMC_vs_Metro |
2
|
1.077
|
0.29
|
0.197
|
| HMC_vs_Metro |
3
|
-0.914
|
0.368
|
-0.167
|
| HMC_vs_Metro |
4
|
-1.097
|
0.282
|
-0.200
|
| HMC_vs_Metro |
5
|
1.022
|
0.315
|
0.187
|
| HMC_vs_DEMetro_Z |
0
|
-1.442
|
0.16
|
-0.263
|
| HMC_vs_DEMetro_Z |
1
|
0.075
|
0.94
|
0.014
|
| HMC_vs_DEMetro_Z |
2
|
0.957
|
0.346
|
0.175
|
| HMC_vs_DEMetro_Z |
3
|
-0.782
|
0.441
|
-0.143
|
| HMC_vs_DEMetro_Z |
4
|
-1.525
|
0.138
|
-0.278
|
| HMC_vs_DEMetro_Z |
5
|
-0.458
|
0.65
|
-0.084
|
| Metro_vs_SMC |
0
|
1.580
|
0.125
|
0.288
|
| Metro_vs_SMC |
1
|
0.246
|
0.807
|
0.045
|
| Metro_vs_SMC |
2
|
4.116
|
0.000292
|
0.751
|
| Metro_vs_SMC |
3
|
2.047
|
0.0498
|
0.374
|
| Metro_vs_SMC |
4
|
1.263
|
0.216
|
0.231
|
| Metro_vs_SMC |
5
|
1.046
|
0.304
|
0.191
|
| DEMetro_Z_vs_SMC |
0
|
2.729
|
0.0107
|
0.498
|
| DEMetro_Z_vs_SMC |
1
|
-1.153
|
0.258
|
-0.210
|
| DEMetro_Z_vs_SMC |
2
|
5.016
|
2.43e-05
|
0.916
|
| DEMetro_Z_vs_SMC |
3
|
4.126
|
0.000284
|
0.753
|
| DEMetro_Z_vs_SMC |
4
|
3.184
|
0.00345
|
0.581
|
| DEMetro_Z_vs_SMC |
5
|
3.138
|
0.00388
|
0.573
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
4.265 |
12.658 |
33.375 |
-0.251 |
| HMC |
8 |
4.190 |
9.038 |
17.720 |
-0.274 |
| HMC |
10 |
8.932 |
15.206 |
35.981 |
-0.174 |
| HMC |
12 |
4.821 |
5.828 |
10.481 |
-0.096 |
| HMC |
15 |
4.735 |
7.481 |
11.222 |
-0.245 |
| HMC |
18 |
14.463 |
72.410 |
371.981 |
-0.156 |
| SMC |
5 |
3.435 |
12.658 |
33.375 |
-0.276 |
| SMC |
8 |
4.964 |
9.038 |
17.720 |
-0.230 |
| SMC |
10 |
3.367 |
15.206 |
35.981 |
-0.329 |
| SMC |
12 |
3.183 |
5.828 |
10.481 |
-0.252 |
| SMC |
15 |
3.388 |
7.481 |
11.222 |
-0.365 |
| SMC |
18 |
6.524 |
72.410 |
371.981 |
-0.177 |
| Metro |
5 |
6.331 |
12.658 |
33.375 |
-0.190 |
| Metro |
8 |
5.353 |
9.038 |
17.720 |
-0.208 |
| Metro |
10 |
4.870 |
15.206 |
35.981 |
-0.287 |
| Metro |
12 |
6.871 |
5.828 |
10.481 |
0.099 |
| Metro |
15 |
13.943 |
7.481 |
11.222 |
0.576 |
| Metro |
18 |
7.723 |
72.410 |
371.981 |
-0.174 |
| DEMetro_Z |
5 |
4.688 |
12.658 |
33.375 |
-0.239 |
| DEMetro_Z |
8 |
4.144 |
9.038 |
17.720 |
-0.276 |
| DEMetro_Z |
10 |
5.241 |
15.206 |
35.981 |
-0.277 |
| DEMetro_Z |
12 |
5.848 |
5.828 |
10.481 |
0.002 |
| DEMetro_Z |
15 |
6.857 |
7.481 |
11.222 |
-0.056 |
| DEMetro_Z |
18 |
17.136 |
72.410 |
371.981 |
-0.149 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
4.024 |
0.000187 |
1.283 |
| HMC |
8 |
4.730 |
3.76e-05 |
2.974 |
| HMC |
10 |
5.720 |
2.58e-06 |
5.130 |
| HMC |
12 |
6.433 |
3.76e-07 |
6.908 |
| HMC |
15 |
4.795 |
4.1e-05 |
6.186 |
| HMC |
18 |
7.224 |
3.19e-08 |
5.745 |
| SMC |
5 |
4.286 |
0.000102 |
1.762 |
| SMC |
8 |
8.278 |
1.24e-09 |
5.485 |
| SMC |
10 |
6.854 |
5.72e-08 |
4.001 |
| SMC |
12 |
6.251 |
5.26e-07 |
5.129 |
| SMC |
15 |
8.234 |
1.98e-09 |
6.535 |
| SMC |
18 |
5.970 |
1.21e-06 |
5.045 |
| Metro |
5 |
5.912 |
6.98e-07 |
2.799 |
| Metro |
8 |
5.131 |
1.16e-05 |
3.286 |
| Metro |
10 |
5.095 |
1.12e-05 |
2.808 |
| Metro |
12 |
3.731 |
0.000779 |
4.245 |
| Metro |
15 |
4.822 |
3.81e-05 |
6.311 |
| Metro |
18 |
4.163 |
0.000242 |
5.479 |
| DEMetro_Z |
5 |
9.534 |
7.77e-13 |
3.176 |
| DEMetro_Z |
8 |
7.741 |
7.26e-09 |
5.972 |
| DEMetro_Z |
10 |
7.862 |
1.45e-09 |
3.698 |
| DEMetro_Z |
12 |
4.948 |
2.77e-05 |
8.286 |
| DEMetro_Z |
15 |
5.346 |
9.45e-06 |
14.894 |
| DEMetro_Z |
18 |
5.584 |
4.87e-06 |
15.230 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-0.759
|
0.454
|
-0.139
|
| Metro_vs_DEMetro_Z |
1
|
-2.531
|
0.017
|
-0.462
|
| Metro_vs_DEMetro_Z |
2
|
-1.367
|
0.182
|
-0.249
|
| Metro_vs_DEMetro_Z |
3
|
-2.098
|
0.0448
|
-0.383
|
| Metro_vs_DEMetro_Z |
4
|
-2.689
|
0.0118
|
-0.491
|
| Metro_vs_DEMetro_Z |
5
|
-3.814
|
0.00066
|
-0.696
|
| DEMetro_Z_vs_SMC |
0
|
3.138
|
0.00389
|
0.573
|
| DEMetro_Z_vs_SMC |
1
|
0.535
|
0.597
|
0.098
|
| DEMetro_Z_vs_SMC |
2
|
-0.419
|
0.678
|
-0.077
|
| DEMetro_Z_vs_SMC |
3
|
1.570
|
0.127
|
0.287
|
| DEMetro_Z_vs_SMC |
4
|
2.991
|
0.00562
|
0.546
|
| DEMetro_Z_vs_SMC |
5
|
3.653
|
0.00102
|
0.667
|
| HMC_vs_DEMetro_Z |
0
|
-6.027
|
1.48e-06
|
-1.100
|
| HMC_vs_DEMetro_Z |
1
|
-3.343
|
0.0023
|
-0.610
|
| HMC_vs_DEMetro_Z |
2
|
1.363
|
0.183
|
0.249
|
| HMC_vs_DEMetro_Z |
3
|
-0.673
|
0.506
|
-0.123
|
| HMC_vs_DEMetro_Z |
4
|
-2.616
|
0.014
|
-0.478
|
| HMC_vs_DEMetro_Z |
5
|
-3.026
|
0.00515
|
-0.552
|
| HMC_vs_Metro |
0
|
-2.817
|
0.00863
|
-0.514
|
| HMC_vs_Metro |
1
|
-0.331
|
0.743
|
-0.060
|
| HMC_vs_Metro |
2
|
2.132
|
0.0416
|
0.389
|
| HMC_vs_Metro |
3
|
1.651
|
0.11
|
0.301
|
| HMC_vs_Metro |
4
|
-0.062
|
0.951
|
-0.011
|
| HMC_vs_Metro |
5
|
0.153
|
0.879
|
0.028
|
| HMC_vs_SMC |
0
|
-1.097
|
0.282
|
-0.200
|
| HMC_vs_SMC |
1
|
-2.577
|
0.0153
|
-0.470
|
| HMC_vs_SMC |
2
|
1.023
|
0.315
|
0.187
|
| HMC_vs_SMC |
3
|
1.488
|
0.148
|
0.272
|
| HMC_vs_SMC |
4
|
-0.228
|
0.821
|
-0.042
|
| HMC_vs_SMC |
5
|
0.613
|
0.545
|
0.112
|
| Metro_vs_SMC |
0
|
1.719
|
0.0962
|
0.314
|
| Metro_vs_SMC |
1
|
-2.210
|
0.0352
|
-0.403
|
| Metro_vs_SMC |
2
|
-2.274
|
0.0305
|
-0.415
|
| Metro_vs_SMC |
3
|
-0.596
|
0.556
|
-0.109
|
| Metro_vs_SMC |
4
|
-0.140
|
0.89
|
-0.026
|
| Metro_vs_SMC |
5
|
0.288
|
0.775
|
0.053
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.194 |
0.131 |
0.049 |
1.283 |
| HMC |
8 |
0.259 |
0.144 |
0.039 |
2.974 |
| HMC |
10 |
0.448 |
0.176 |
0.053 |
5.130 |
| HMC |
12 |
0.541 |
0.162 |
0.055 |
6.908 |
| HMC |
15 |
0.586 |
0.184 |
0.065 |
6.186 |
| HMC |
18 |
0.834 |
0.192 |
0.112 |
5.745 |
| SMC |
5 |
0.217 |
0.131 |
0.049 |
1.762 |
| SMC |
8 |
0.356 |
0.144 |
0.039 |
5.485 |
| SMC |
10 |
0.388 |
0.176 |
0.053 |
4.001 |
| SMC |
12 |
0.443 |
0.162 |
0.055 |
5.129 |
| SMC |
15 |
0.609 |
0.184 |
0.065 |
6.535 |
| SMC |
18 |
0.755 |
0.192 |
0.112 |
5.045 |
| Metro |
5 |
0.268 |
0.131 |
0.049 |
2.799 |
| Metro |
8 |
0.271 |
0.144 |
0.039 |
3.286 |
| Metro |
10 |
0.325 |
0.176 |
0.053 |
2.808 |
| Metro |
12 |
0.395 |
0.162 |
0.055 |
4.245 |
| Metro |
15 |
0.595 |
0.184 |
0.065 |
6.311 |
| Metro |
18 |
0.804 |
0.192 |
0.112 |
5.479 |
| DEMetro_Z |
5 |
0.287 |
0.131 |
0.049 |
3.176 |
| DEMetro_Z |
8 |
0.375 |
0.144 |
0.039 |
5.972 |
| DEMetro_Z |
10 |
0.372 |
0.176 |
0.053 |
3.698 |
| DEMetro_Z |
12 |
0.616 |
0.162 |
0.055 |
8.286 |
| DEMetro_Z |
15 |
1.153 |
0.184 |
0.065 |
14.894 |
| DEMetro_Z |
18 |
1.893 |
0.192 |
0.112 |
15.230 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
5 |
5.123 |
1.18e-05 |
3.291 |
| HMC |
8 |
4.403 |
0.000122 |
5.096 |
| HMC |
10 |
5.408 |
6.81e-06 |
5.725 |
| HMC |
12 |
6.853 |
1.16e-07 |
7.283 |
| HMC |
15 |
4.684 |
5.72e-05 |
6.873 |
| HMC |
18 |
6.823 |
1.6e-07 |
15.272 |
| SMC |
5 |
4.981 |
2.09e-05 |
4.077 |
| SMC |
8 |
6.152 |
8.62e-07 |
7.281 |
| SMC |
10 |
5.959 |
1.17e-06 |
4.642 |
| SMC |
12 |
5.562 |
4.07e-06 |
4.977 |
| SMC |
15 |
6.640 |
2.02e-07 |
6.696 |
| SMC |
18 |
5.009 |
2.42e-05 |
14.170 |
| Metro |
5 |
6.292 |
3.74e-07 |
4.187 |
| Metro |
8 |
6.766 |
9.02e-08 |
4.417 |
| Metro |
10 |
4.677 |
4.22e-05 |
2.754 |
| Metro |
12 |
2.533 |
0.0168 |
3.776 |
| Metro |
15 |
5.972 |
1.15e-06 |
4.782 |
| Metro |
18 |
3.826 |
0.000637 |
16.098 |
| DEMetro_Z |
5 |
13.505 |
3.54e-17 |
5.349 |
| DEMetro_Z |
8 |
7.171 |
4.91e-08 |
7.796 |
| DEMetro_Z |
10 |
6.556 |
1.22e-07 |
3.560 |
| DEMetro_Z |
12 |
4.179 |
0.000238 |
8.044 |
| DEMetro_Z |
15 |
4.931 |
3.03e-05 |
16.453 |
| DEMetro_Z |
18 |
5.149 |
1.67e-05 |
46.598 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
1.450
|
0.158
|
0.265
|
| DEMetro_Z_vs_SMC |
1
|
0.316
|
0.754
|
0.058
|
| DEMetro_Z_vs_SMC |
2
|
-1.145
|
0.261
|
-0.209
|
| DEMetro_Z_vs_SMC |
3
|
1.345
|
0.189
|
0.246
|
| DEMetro_Z_vs_SMC |
4
|
2.861
|
0.00776
|
0.522
|
| DEMetro_Z_vs_SMC |
5
|
3.427
|
0.00184
|
0.626
|
| HMC_vs_Metro |
0
|
-0.900
|
0.375
|
-0.164
|
| HMC_vs_Metro |
1
|
0.505
|
0.618
|
0.092
|
| HMC_vs_Metro |
2
|
2.273
|
0.0306
|
0.415
|
| HMC_vs_Metro |
3
|
1.864
|
0.0724
|
0.340
|
| HMC_vs_Metro |
4
|
1.139
|
0.264
|
0.208
|
| HMC_vs_Metro |
5
|
-0.153
|
0.88
|
-0.028
|
| Metro_vs_DEMetro_Z |
0
|
-1.545
|
0.133
|
-0.282
|
| Metro_vs_DEMetro_Z |
1
|
-2.635
|
0.0134
|
-0.481
|
| Metro_vs_DEMetro_Z |
2
|
-1.119
|
0.272
|
-0.204
|
| Metro_vs_DEMetro_Z |
3
|
-1.765
|
0.0881
|
-0.322
|
| Metro_vs_DEMetro_Z |
4
|
-3.418
|
0.00189
|
-0.624
|
| Metro_vs_DEMetro_Z |
5
|
-3.613
|
0.00113
|
-0.660
|
| HMC_vs_SMC |
0
|
-0.777
|
0.444
|
-0.142
|
| HMC_vs_SMC |
1
|
-1.203
|
0.239
|
-0.220
|
| HMC_vs_SMC |
2
|
0.777
|
0.443
|
0.142
|
| HMC_vs_SMC |
3
|
1.855
|
0.0738
|
0.339
|
| HMC_vs_SMC |
4
|
0.097
|
0.923
|
0.018
|
| HMC_vs_SMC |
5
|
0.297
|
0.769
|
0.054
|
| Metro_vs_SMC |
0
|
0.099
|
0.922
|
0.018
|
| Metro_vs_SMC |
1
|
-1.986
|
0.0566
|
-0.363
|
| Metro_vs_SMC |
2
|
-2.420
|
0.022
|
-0.442
|
| Metro_vs_SMC |
3
|
-0.649
|
0.522
|
-0.118
|
| Metro_vs_SMC |
4
|
-1.466
|
0.153
|
-0.268
|
| Metro_vs_SMC |
5
|
0.383
|
0.705
|
0.070
|
| HMC_vs_DEMetro_Z |
0
|
-2.812
|
0.00875
|
-0.513
|
| HMC_vs_DEMetro_Z |
1
|
-1.804
|
0.0816
|
-0.329
|
| HMC_vs_DEMetro_Z |
2
|
1.834
|
0.077
|
0.335
|
| HMC_vs_DEMetro_Z |
3
|
-0.330
|
0.743
|
-0.060
|
| HMC_vs_DEMetro_Z |
4
|
-2.429
|
0.0216
|
-0.443
|
| HMC_vs_DEMetro_Z |
5
|
-3.029
|
0.00512
|
-0.553
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
5 |
0.026 |
0.012 |
0.004 |
3.291 |
| HMC |
8 |
0.031 |
0.011 |
0.004 |
5.096 |
| HMC |
10 |
0.053 |
0.013 |
0.007 |
5.725 |
| HMC |
12 |
0.063 |
0.012 |
0.007 |
7.283 |
| HMC |
15 |
0.058 |
0.012 |
0.007 |
6.873 |
| HMC |
18 |
0.069 |
0.009 |
0.004 |
15.272 |
| SMC |
5 |
0.030 |
0.012 |
0.004 |
4.077 |
| SMC |
8 |
0.040 |
0.011 |
0.004 |
7.281 |
| SMC |
10 |
0.045 |
0.013 |
0.007 |
4.642 |
| SMC |
12 |
0.047 |
0.012 |
0.007 |
4.977 |
| SMC |
15 |
0.057 |
0.012 |
0.007 |
6.696 |
| SMC |
18 |
0.065 |
0.009 |
0.004 |
14.170 |
| Metro |
5 |
0.030 |
0.012 |
0.004 |
4.187 |
| Metro |
8 |
0.029 |
0.011 |
0.004 |
4.417 |
| Metro |
10 |
0.032 |
0.013 |
0.007 |
2.754 |
| Metro |
12 |
0.038 |
0.012 |
0.007 |
3.776 |
| Metro |
15 |
0.044 |
0.012 |
0.007 |
4.782 |
| Metro |
18 |
0.072 |
0.009 |
0.004 |
16.098 |
| DEMetro_Z |
5 |
0.035 |
0.012 |
0.004 |
5.349 |
| DEMetro_Z |
8 |
0.042 |
0.011 |
0.004 |
7.796 |
| DEMetro_Z |
10 |
0.038 |
0.013 |
0.007 |
3.560 |
| DEMetro_Z |
12 |
0.069 |
0.012 |
0.007 |
8.044 |
| DEMetro_Z |
15 |
0.123 |
0.012 |
0.007 |
16.453 |
| DEMetro_Z |
18 |
0.192 |
0.009 |
0.004 |
46.598 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
Mode Transitions (scatter)
KDE + Init Plots
Trace Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Varying_Tails_with_high_Dimension
(MvStudentT,
nu,
30 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
2.036 |
0.0507 |
3.524 |
| HMC |
3.0 |
1.395 |
0.173 |
2.640 |
| HMC |
4.0 |
0.175 |
0.863 |
0.128 |
| HMC |
10.0 |
-2.814 |
0.00674 |
-0.667 |
| HMC |
50.0 |
-4.256 |
8.01e-05 |
-1.008 |
| SMC |
2.1 |
52.414 |
3.61e-31 |
68.951 |
| SMC |
3.0 |
39.400 |
3.72e-27 |
69.167 |
| SMC |
4.0 |
29.632 |
2.06e-23 |
72.257 |
| SMC |
10.0 |
39.163 |
2.17e-27 |
52.185 |
| SMC |
50.0 |
23.260 |
3.35e-21 |
23.047 |
| Metro |
2.1 |
2.616 |
0.014 |
22.000 |
| Metro |
3.0 |
11.205 |
9.1e-13 |
8.143 |
| Metro |
4.0 |
13.972 |
1.47e-15 |
9.364 |
| Metro |
10.0 |
18.394 |
2.28e-21 |
8.009 |
| Metro |
50.0 |
15.200 |
2.64e-18 |
6.735 |
| DEMetro_Z |
2.1 |
23.648 |
1.66e-20 |
366.943 |
| DEMetro_Z |
3.0 |
21.050 |
4.07e-19 |
413.531 |
| DEMetro_Z |
4.0 |
25.177 |
2.93e-21 |
436.403 |
| DEMetro_Z |
10.0 |
24.472 |
6.38e-21 |
273.772 |
| DEMetro_Z |
50.0 |
13.268 |
7.59e-14 |
286.124 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-22.716
|
5.07e-20
|
-4.147
|
| HMC_vs_DEMetro_Z |
1
|
-21.072
|
3.97e-19
|
-3.847
|
| HMC_vs_DEMetro_Z |
2
|
-25.418
|
2.26e-21
|
-4.641
|
| HMC_vs_DEMetro_Z |
3
|
-24.437
|
6.75e-21
|
-4.462
|
| HMC_vs_DEMetro_Z |
4
|
-13.307
|
7.06e-14
|
-2.430
|
| Metro_vs_SMC |
0
|
-5.473
|
6.81e-06
|
-0.999
|
| Metro_vs_SMC |
1
|
-29.536
|
3.41e-23
|
-5.392
|
| Metro_vs_SMC |
2
|
-24.709
|
4.97e-21
|
-4.511
|
| Metro_vs_SMC |
3
|
-33.992
|
6.47e-25
|
-6.206
|
| Metro_vs_SMC |
4
|
-17.285
|
8.21e-17
|
-3.156
|
| Metro_vs_DEMetro_Z |
0
|
-19.651
|
2.64e-18
|
-3.588
|
| Metro_vs_DEMetro_Z |
1
|
-20.438
|
9.12e-19
|
-3.731
|
| Metro_vs_DEMetro_Z |
2
|
-24.965
|
3.73e-21
|
-4.558
|
| Metro_vs_DEMetro_Z |
3
|
-23.709
|
1.56e-20
|
-4.329
|
| Metro_vs_DEMetro_Z |
4
|
-12.949
|
1.4e-13
|
-2.364
|
| HMC_vs_Metro |
0
|
-2.163
|
0.0389
|
-0.395
|
| HMC_vs_Metro |
1
|
-2.915
|
0.00679
|
-0.532
|
| HMC_vs_Metro |
2
|
-9.697
|
1.32e-10
|
-1.770
|
| HMC_vs_Metro |
3
|
-19.805
|
2.14e-18
|
-3.616
|
| HMC_vs_Metro |
4
|
-18.671
|
1.05e-17
|
-3.409
|
| HMC_vs_SMC |
0
|
-28.730
|
7.4e-23
|
-5.245
|
| HMC_vs_SMC |
1
|
-23.165
|
2.96e-20
|
-4.229
|
| HMC_vs_SMC |
2
|
-29.102
|
5.16e-23
|
-5.313
|
| HMC_vs_SMC |
3
|
-39.437
|
9.51e-27
|
-7.200
|
| HMC_vs_SMC |
4
|
-24.927
|
3.89e-21
|
-4.551
|
| DEMetro_Z_vs_SMC |
0
|
19.300
|
4.3e-18
|
3.524
|
| DEMetro_Z_vs_SMC |
1
|
18.254
|
1.92e-17
|
3.333
|
| DEMetro_Z_vs_SMC |
2
|
20.730
|
6.2e-19
|
3.785
|
| DEMetro_Z_vs_SMC |
3
|
20.244
|
1.18e-18
|
3.696
|
| DEMetro_Z_vs_SMC |
4
|
12.227
|
5.74e-13
|
2.232
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.148 |
0.070 |
0.022 |
3.524 |
| HMC |
3.0 |
0.053 |
0.038 |
0.005 |
2.640 |
| HMC |
4.0 |
0.033 |
0.032 |
0.004 |
0.128 |
| HMC |
10.0 |
0.022 |
0.024 |
0.003 |
-0.667 |
| HMC |
50.0 |
0.020 |
0.022 |
0.003 |
-1.008 |
| SMC |
2.1 |
1.602 |
0.070 |
0.022 |
68.951 |
| SMC |
3.0 |
0.415 |
0.038 |
0.005 |
69.167 |
| SMC |
4.0 |
0.309 |
0.032 |
0.004 |
72.257 |
| SMC |
10.0 |
0.195 |
0.024 |
0.003 |
52.185 |
| SMC |
50.0 |
0.088 |
0.022 |
0.003 |
23.047 |
| Metro |
2.1 |
0.559 |
0.070 |
0.022 |
22.000 |
| Metro |
3.0 |
0.083 |
0.038 |
0.005 |
8.143 |
| Metro |
4.0 |
0.068 |
0.032 |
0.004 |
9.364 |
| Metro |
10.0 |
0.050 |
0.024 |
0.003 |
8.009 |
| Metro |
50.0 |
0.042 |
0.022 |
0.003 |
6.735 |
| DEMetro_Z |
2.1 |
8.224 |
0.070 |
0.022 |
366.943 |
| DEMetro_Z |
3.0 |
2.292 |
0.038 |
0.005 |
413.531 |
| DEMetro_Z |
4.0 |
1.705 |
0.032 |
0.004 |
436.403 |
| DEMetro_Z |
10.0 |
0.922 |
0.024 |
0.003 |
273.772 |
| DEMetro_Z |
50.0 |
0.836 |
0.022 |
0.003 |
286.124 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
-0.911 |
0.368 |
-0.176 |
| HMC |
3.0 |
1.073 |
0.29 |
0.592 |
| HMC |
4.0 |
2.812 |
0.0067 |
0.722 |
| HMC |
10.0 |
5.779 |
1.09e-06 |
2.776 |
| HMC |
50.0 |
10.082 |
2.59e-13 |
3.643 |
| SMC |
2.1 |
217.095 |
1.25e-52 |
171.585 |
| SMC |
3.0 |
220.335 |
9.99e-50 |
306.734 |
| SMC |
4.0 |
160.497 |
2.38e-44 |
1475.303 |
| SMC |
10.0 |
120.910 |
9.29e-41 |
12818.266 |
| SMC |
50.0 |
53.938 |
1.22e-30 |
1713.122 |
| Metro |
2.1 |
1.113 |
0.275 |
34.033 |
| Metro |
3.0 |
1.965 |
0.0545 |
0.453 |
| Metro |
4.0 |
5.049 |
7.87e-06 |
1.923 |
| Metro |
10.0 |
13.387 |
9.46e-15 |
10.380 |
| Metro |
50.0 |
17.249 |
1.52e-19 |
8.530 |
| DEMetro_Z |
2.1 |
15.288 |
1.86e-15 |
55.358 |
| DEMetro_Z |
3.0 |
12.112 |
7.02e-13 |
68.168 |
| DEMetro_Z |
4.0 |
12.787 |
1.9e-13 |
308.941 |
| DEMetro_Z |
10.0 |
15.533 |
1.36e-15 |
1628.366 |
| DEMetro_Z |
50.0 |
7.605 |
2.2e-08 |
1758.242 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
-219.139
|
3.07e-48
|
-40.009
|
| HMC_vs_SMC |
1
|
-206.060
|
1.83e-47
|
-37.621
|
| HMC_vs_SMC |
2
|
-160.629
|
2.49e-44
|
-29.327
|
| HMC_vs_SMC |
3
|
-120.885
|
9.35e-41
|
-22.071
|
| HMC_vs_SMC |
4
|
-53.838
|
1.29e-30
|
-9.829
|
| Metro_vs_DEMetro_Z |
0
|
-0.707
|
0.485
|
-0.129
|
| Metro_vs_DEMetro_Z |
1
|
-12.024
|
8.64e-13
|
-2.195
|
| Metro_vs_DEMetro_Z |
2
|
-12.738
|
2.1e-13
|
-2.326
|
| Metro_vs_DEMetro_Z |
3
|
-15.420
|
1.64e-15
|
-2.815
|
| Metro_vs_DEMetro_Z |
4
|
-7.575
|
2.37e-08
|
-1.383
|
| HMC_vs_Metro |
0
|
-1.119
|
0.272
|
-0.204
|
| HMC_vs_Metro |
1
|
0.267
|
0.791
|
0.049
|
| HMC_vs_Metro |
2
|
-3.618
|
0.00112
|
-0.661
|
| HMC_vs_Metro |
3
|
-8.249
|
4.28e-09
|
-1.506
|
| HMC_vs_Metro |
4
|
-9.622
|
1.57e-10
|
-1.757
|
| HMC_vs_DEMetro_Z |
0
|
-15.376
|
1.77e-15
|
-2.807
|
| HMC_vs_DEMetro_Z |
1
|
-11.941
|
1.02e-12
|
-2.180
|
| HMC_vs_DEMetro_Z |
2
|
-12.769
|
1.97e-13
|
-2.331
|
| HMC_vs_DEMetro_Z |
3
|
-15.477
|
1.49e-15
|
-2.826
|
| HMC_vs_DEMetro_Z |
4
|
-7.591
|
2.28e-08
|
-1.386
|
| Metro_vs_SMC |
0
|
-4.488
|
0.000105
|
-0.819
|
| Metro_vs_SMC |
1
|
-233.163
|
5.09e-49
|
-42.570
|
| Metro_vs_SMC |
2
|
-161.346
|
2.19e-44
|
-29.458
|
| Metro_vs_SMC |
3
|
-120.500
|
1.03e-40
|
-22.000
|
| Metro_vs_SMC |
4
|
-53.629
|
1.44e-30
|
-9.791
|
| DEMetro_Z_vs_SMC |
0
|
-33.538
|
9.47e-25
|
-6.123
|
| DEMetro_Z_vs_SMC |
1
|
-42.072
|
1.5e-27
|
-7.681
|
| DEMetro_Z_vs_SMC |
2
|
-40.216
|
5.44e-27
|
-7.342
|
| DEMetro_Z_vs_SMC |
3
|
-88.123
|
8.74e-37
|
-16.089
|
| DEMetro_Z_vs_SMC |
4
|
0.191
|
0.85
|
0.035
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
6.357 |
9.489 |
17.780 |
-0.176 |
| HMC |
3.0 |
1.336 |
0.749 |
0.992 |
0.592 |
| HMC |
4.0 |
0.283 |
0.190 |
0.128 |
0.722 |
| HMC |
10.0 |
0.068 |
0.050 |
0.007 |
2.776 |
| HMC |
50.0 |
0.047 |
0.033 |
0.004 |
3.643 |
| SMC |
2.1 |
3060.211 |
9.489 |
17.780 |
171.585 |
| SMC |
3.0 |
304.990 |
0.749 |
0.992 |
306.734 |
| SMC |
4.0 |
188.910 |
0.190 |
0.128 |
1475.303 |
| SMC |
10.0 |
86.778 |
0.050 |
0.007 |
12818.266 |
| SMC |
50.0 |
6.641 |
0.033 |
0.004 |
1713.122 |
| Metro |
2.1 |
614.587 |
9.489 |
17.780 |
34.033 |
| Metro |
3.0 |
1.198 |
0.749 |
0.992 |
0.453 |
| Metro |
4.0 |
0.436 |
0.190 |
0.128 |
1.923 |
| Metro |
10.0 |
0.120 |
0.050 |
0.007 |
10.380 |
| Metro |
50.0 |
0.065 |
0.033 |
0.004 |
8.530 |
| DEMetro_Z |
2.1 |
993.734 |
9.489 |
17.780 |
55.358 |
| DEMetro_Z |
3.0 |
68.363 |
0.749 |
0.992 |
68.168 |
| DEMetro_Z |
4.0 |
39.710 |
0.190 |
0.128 |
308.941 |
| DEMetro_Z |
10.0 |
11.067 |
0.050 |
0.007 |
1628.366 |
| DEMetro_Z |
50.0 |
6.815 |
0.033 |
0.004 |
1758.242 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
5.508 |
5.6e-06 |
8.039 |
| HMC |
3.0 |
3.809 |
0.000666 |
13.667 |
| HMC |
4.0 |
4.749 |
4.71e-05 |
6.431 |
| HMC |
10.0 |
3.651 |
0.000598 |
1.130 |
| HMC |
50.0 |
1.658 |
0.103 |
0.399 |
| SMC |
2.1 |
411.458 |
1.98e-56 |
1456.165 |
| SMC |
3.0 |
396.793 |
8.3e-56 |
2330.328 |
| SMC |
4.0 |
287.941 |
1.04e-51 |
2802.889 |
| SMC |
10.0 |
215.657 |
4.78e-48 |
3605.540 |
| SMC |
50.0 |
78.550 |
2.34e-35 |
898.044 |
| Metro |
2.1 |
2.909 |
0.0069 |
94.373 |
| Metro |
3.0 |
9.016 |
5.96e-10 |
22.671 |
| Metro |
4.0 |
13.621 |
1.97e-14 |
17.479 |
| Metro |
10.0 |
21.292 |
4.73e-21 |
14.422 |
| Metro |
50.0 |
19.315 |
5.81e-21 |
9.967 |
| DEMetro_Z |
2.1 |
31.534 |
5.37e-24 |
760.442 |
| DEMetro_Z |
3.0 |
25.646 |
1.76e-21 |
950.354 |
| DEMetro_Z |
4.0 |
25.147 |
3.05e-21 |
1066.783 |
| DEMetro_Z |
10.0 |
25.412 |
2.28e-21 |
976.773 |
| DEMetro_Z |
50.0 |
15.458 |
1.54e-15 |
737.343 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-18.082
|
2.47e-17
|
-3.301
|
| Metro_vs_DEMetro_Z |
1
|
-24.765
|
4.67e-21
|
-4.521
|
| Metro_vs_DEMetro_Z |
2
|
-25.010
|
3.55e-21
|
-4.566
|
| Metro_vs_DEMetro_Z |
3
|
-24.895
|
4.03e-21
|
-4.545
|
| Metro_vs_DEMetro_Z |
4
|
-15.237
|
2.24e-15
|
-2.782
|
| DEMetro_Z_vs_SMC |
0
|
-30.109
|
1.98e-23
|
-5.497
|
| DEMetro_Z_vs_SMC |
1
|
-37.429
|
4.2e-26
|
-6.834
|
| DEMetro_Z_vs_SMC |
2
|
-37.033
|
5.69e-26
|
-6.761
|
| DEMetro_Z_vs_SMC |
3
|
-71.450
|
3.73e-34
|
-13.045
|
| DEMetro_Z_vs_SMC |
4
|
-3.253
|
0.0029
|
-0.594
|
| HMC_vs_DEMetro_Z |
0
|
-30.640
|
1.21e-23
|
-5.594
|
| HMC_vs_DEMetro_Z |
1
|
-25.797
|
1.5e-21
|
-4.710
|
| HMC_vs_DEMetro_Z |
2
|
-25.189
|
2.91e-21
|
-4.599
|
| HMC_vs_DEMetro_Z |
3
|
-25.302
|
2.57e-21
|
-4.619
|
| HMC_vs_DEMetro_Z |
4
|
-15.451
|
1.56e-15
|
-2.821
|
| HMC_vs_Metro |
0
|
-2.658
|
0.0127
|
-0.485
|
| HMC_vs_Metro |
1
|
-1.990
|
0.056
|
-0.363
|
| HMC_vs_Metro |
2
|
-5.947
|
1.84e-06
|
-1.086
|
| HMC_vs_Metro |
3
|
-21.232
|
3.23e-19
|
-3.876
|
| HMC_vs_Metro |
4
|
-19.365
|
3.93e-18
|
-3.536
|
| HMC_vs_SMC |
0
|
-324.356
|
3.55e-53
|
-59.219
|
| HMC_vs_SMC |
1
|
-331.172
|
1.94e-53
|
-60.463
|
| HMC_vs_SMC |
2
|
-280.645
|
2.36e-51
|
-51.239
|
| HMC_vs_SMC |
3
|
-215.143
|
5.23e-48
|
-39.280
|
| HMC_vs_SMC |
4
|
-78.561
|
2.41e-35
|
-14.343
|
| Metro_vs_SMC |
0
|
-41.364
|
2.44e-27
|
-7.552
|
| Metro_vs_SMC |
1
|
-403.779
|
6.2e-56
|
-73.720
|
| Metro_vs_SMC |
2
|
-288.990
|
1.01e-51
|
-52.762
|
| Metro_vs_SMC |
3
|
-210.827
|
9.42e-48
|
-38.492
|
| Metro_vs_SMC |
4
|
-77.608
|
3.43e-35
|
-14.169
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.353 |
0.118 |
0.029 |
8.039 |
| HMC |
3.0 |
0.140 |
0.065 |
0.005 |
13.667 |
| HMC |
4.0 |
0.072 |
0.050 |
0.004 |
6.431 |
| HMC |
10.0 |
0.036 |
0.034 |
0.002 |
1.130 |
| HMC |
50.0 |
0.030 |
0.029 |
0.002 |
0.399 |
| SMC |
2.1 |
42.600 |
0.118 |
0.029 |
1456.165 |
| SMC |
3.0 |
12.875 |
0.065 |
0.005 |
2330.328 |
| SMC |
4.0 |
9.996 |
0.050 |
0.004 |
2802.889 |
| SMC |
10.0 |
6.616 |
0.034 |
0.002 |
3605.540 |
| SMC |
50.0 |
1.402 |
0.029 |
0.002 |
898.044 |
| Metro |
2.1 |
2.871 |
0.118 |
0.029 |
94.373 |
| Metro |
3.0 |
0.190 |
0.065 |
0.005 |
22.671 |
| Metro |
4.0 |
0.112 |
0.050 |
0.004 |
17.479 |
| Metro |
10.0 |
0.060 |
0.034 |
0.002 |
14.422 |
| Metro |
50.0 |
0.045 |
0.029 |
0.002 |
9.967 |
| DEMetro_Z |
2.1 |
22.303 |
0.118 |
0.029 |
760.442 |
| DEMetro_Z |
3.0 |
5.289 |
0.065 |
0.005 |
950.354 |
| DEMetro_Z |
4.0 |
3.835 |
0.050 |
0.004 |
1066.783 |
| DEMetro_Z |
10.0 |
1.817 |
0.034 |
0.002 |
976.773 |
| DEMetro_Z |
50.0 |
1.156 |
0.029 |
0.002 |
737.343 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
5.269 |
1.2e-05 |
41.277 |
| HMC |
3.0 |
4.329 |
0.000161 |
15.287 |
| HMC |
4.0 |
4.387 |
0.000132 |
6.652 |
| HMC |
10.0 |
2.072 |
0.0428 |
0.589 |
| HMC |
50.0 |
0.145 |
0.885 |
0.034 |
| SMC |
2.1 |
222.478 |
2.03e-50 |
262.694 |
| SMC |
3.0 |
223.897 |
1.08e-50 |
252.788 |
| SMC |
4.0 |
239.733 |
2.06e-51 |
282.636 |
| SMC |
10.0 |
189.530 |
9.7e-48 |
266.335 |
| SMC |
50.0 |
190.984 |
1.57e-48 |
218.442 |
| Metro |
2.1 |
13.442 |
5.43e-14 |
148.206 |
| Metro |
3.0 |
9.054 |
5.54e-10 |
25.608 |
| Metro |
4.0 |
15.419 |
6.97e-16 |
19.140 |
| Metro |
10.0 |
20.655 |
5.29e-22 |
10.577 |
| Metro |
50.0 |
18.449 |
1.99e-21 |
8.021 |
| DEMetro_Z |
2.1 |
79.410 |
1.35e-35 |
314.895 |
| DEMetro_Z |
3.0 |
81.241 |
6.41e-36 |
283.466 |
| DEMetro_Z |
4.0 |
115.748 |
1.71e-40 |
320.607 |
| DEMetro_Z |
10.0 |
62.055 |
1.77e-32 |
270.040 |
| DEMetro_Z |
50.0 |
38.064 |
2.45e-26 |
257.261 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
12.041
|
8.35e-13
|
2.198
|
| DEMetro_Z_vs_SMC |
1
|
8.554
|
2.01e-09
|
1.562
|
| DEMetro_Z_vs_SMC |
2
|
12.265
|
5.32e-13
|
2.239
|
| DEMetro_Z_vs_SMC |
3
|
0.806
|
0.427
|
0.147
|
| DEMetro_Z_vs_SMC |
4
|
5.585
|
5e-06
|
1.020
|
| HMC_vs_Metro |
0
|
-7.668
|
1.87e-08
|
-1.400
|
| HMC_vs_Metro |
1
|
-2.096
|
0.0449
|
-0.383
|
| HMC_vs_Metro |
2
|
-5.613
|
4.62e-06
|
-1.025
|
| HMC_vs_Metro |
3
|
-21.209
|
3.33e-19
|
-3.872
|
| HMC_vs_Metro |
4
|
-19.528
|
3.13e-18
|
-3.565
|
| Metro_vs_DEMetro_Z |
0
|
-14.943
|
3.71e-15
|
-2.728
|
| Metro_vs_DEMetro_Z |
1
|
-51.750
|
4.01e-30
|
-9.448
|
| Metro_vs_DEMetro_Z |
2
|
-113.479
|
5.83e-40
|
-20.718
|
| Metro_vs_DEMetro_Z |
3
|
-57.252
|
2.2e-31
|
-10.453
|
| Metro_vs_DEMetro_Z |
4
|
-36.685
|
7.44e-26
|
-6.698
|
| HMC_vs_SMC |
0
|
-29.686
|
2.95e-23
|
-5.420
|
| HMC_vs_SMC |
1
|
-68.618
|
1.2e-33
|
-12.528
|
| HMC_vs_SMC |
2
|
-135.173
|
3.68e-42
|
-24.679
|
| HMC_vs_SMC |
3
|
-188.623
|
2.37e-46
|
-34.438
|
| HMC_vs_SMC |
4
|
-196.814
|
6.91e-47
|
-35.933
|
| Metro_vs_SMC |
0
|
-10.557
|
1.9e-11
|
-1.927
|
| Metro_vs_SMC |
1
|
-67.681
|
1.78e-33
|
-12.357
|
| Metro_vs_SMC |
2
|
-160.164
|
2.71e-44
|
-29.242
|
| Metro_vs_SMC |
3
|
-172.836
|
2.98e-45
|
-31.555
|
| Metro_vs_SMC |
4
|
-182.097
|
6.57e-46
|
-33.246
|
| HMC_vs_DEMetro_Z |
0
|
-31.432
|
5.91e-24
|
-5.739
|
| HMC_vs_DEMetro_Z |
1
|
-65.652
|
4.27e-33
|
-11.986
|
| HMC_vs_DEMetro_Z |
2
|
-108.202
|
2.31e-39
|
-19.755
|
| HMC_vs_DEMetro_Z |
3
|
-60.110
|
5.41e-32
|
-10.975
|
| HMC_vs_DEMetro_Z |
4
|
-38.101
|
2.54e-26
|
-6.956
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.077 |
0.015 |
0.001 |
41.277 |
| HMC |
3.0 |
0.039 |
0.015 |
0.002 |
15.287 |
| HMC |
4.0 |
0.024 |
0.015 |
0.001 |
6.652 |
| HMC |
10.0 |
0.015 |
0.014 |
0.001 |
0.589 |
| HMC |
50.0 |
0.014 |
0.014 |
0.001 |
0.034 |
| SMC |
2.1 |
0.409 |
0.015 |
0.001 |
262.694 |
| SMC |
3.0 |
0.406 |
0.015 |
0.002 |
252.788 |
| SMC |
4.0 |
0.399 |
0.015 |
0.001 |
282.636 |
| SMC |
10.0 |
0.398 |
0.014 |
0.001 |
266.335 |
| SMC |
50.0 |
0.307 |
0.014 |
0.001 |
218.442 |
| Metro |
2.1 |
0.237 |
0.015 |
0.001 |
148.206 |
| Metro |
3.0 |
0.055 |
0.015 |
0.002 |
25.608 |
| Metro |
4.0 |
0.041 |
0.015 |
0.001 |
19.140 |
| Metro |
10.0 |
0.029 |
0.014 |
0.001 |
10.577 |
| Metro |
50.0 |
0.025 |
0.014 |
0.001 |
8.021 |
| DEMetro_Z |
2.1 |
0.487 |
0.015 |
0.001 |
314.895 |
| DEMetro_Z |
3.0 |
0.453 |
0.015 |
0.002 |
283.466 |
| DEMetro_Z |
4.0 |
0.450 |
0.015 |
0.001 |
320.607 |
| DEMetro_Z |
10.0 |
0.403 |
0.014 |
0.001 |
270.040 |
| DEMetro_Z |
50.0 |
0.359 |
0.014 |
0.001 |
257.261 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
1.763 |
0.0881 |
2.965 |
| HMC |
3.0 |
0.844 |
0.404 |
0.438 |
| HMC |
4.0 |
-0.388 |
0.701 |
-0.272 |
| HMC |
10.0 |
-3.085 |
0.00319 |
-0.713 |
| HMC |
50.0 |
-3.755 |
0.000419 |
-0.876 |
| SMC |
2.1 |
35.799 |
5.64e-26 |
60.674 |
| SMC |
3.0 |
28.504 |
5.93e-23 |
65.762 |
| SMC |
4.0 |
23.092 |
2.61e-20 |
70.823 |
| SMC |
10.0 |
26.394 |
3.75e-22 |
45.541 |
| SMC |
50.0 |
23.375 |
6.98e-22 |
17.937 |
| Metro |
2.1 |
6.151 |
9.17e-07 |
8.726 |
| Metro |
3.0 |
14.775 |
2.02e-17 |
7.150 |
| Metro |
4.0 |
11.351 |
7.54e-13 |
8.657 |
| Metro |
10.0 |
18.007 |
8.5e-21 |
8.097 |
| Metro |
50.0 |
18.052 |
1.42e-22 |
6.617 |
| DEMetro_Z |
2.1 |
18.976 |
6.76e-18 |
347.184 |
| DEMetro_Z |
3.0 |
17.879 |
3.33e-17 |
359.552 |
| DEMetro_Z |
4.0 |
19.720 |
2.4e-18 |
409.903 |
| DEMetro_Z |
10.0 |
12.874 |
1.61e-13 |
304.126 |
| DEMetro_Z |
50.0 |
11.085 |
6.05e-12 |
209.480 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-19.248
|
4.63e-18
|
-3.514
|
| HMC_vs_DEMetro_Z |
1
|
-17.849
|
3.5e-17
|
-3.259
|
| HMC_vs_DEMetro_Z |
2
|
-19.931
|
1.8e-18
|
-3.639
|
| HMC_vs_DEMetro_Z |
3
|
-12.906
|
1.52e-13
|
-2.356
|
| HMC_vs_DEMetro_Z |
4
|
-11.164
|
5.13e-12
|
-2.038
|
| Metro_vs_SMC |
0
|
-21.521
|
2.23e-19
|
-3.929
|
| Metro_vs_SMC |
1
|
-23.920
|
1.22e-20
|
-4.367
|
| Metro_vs_SMC |
2
|
-23.574
|
1.82e-20
|
-4.304
|
| Metro_vs_SMC |
3
|
-21.576
|
2.08e-19
|
-3.939
|
| Metro_vs_SMC |
4
|
-13.353
|
6.48e-14
|
-2.438
|
| Metro_vs_DEMetro_Z |
0
|
-18.565
|
1.22e-17
|
-3.390
|
| Metro_vs_DEMetro_Z |
1
|
-17.624
|
4.91e-17
|
-3.218
|
| Metro_vs_DEMetro_Z |
2
|
-19.287
|
4.38e-18
|
-3.521
|
| Metro_vs_DEMetro_Z |
3
|
-12.507
|
3.3e-13
|
-2.283
|
| Metro_vs_DEMetro_Z |
4
|
-10.801
|
1.12e-11
|
-1.972
|
| HMC_vs_Metro |
0
|
-2.439
|
0.0211
|
-0.445
|
| HMC_vs_Metro |
1
|
-11.277
|
4.04e-12
|
-2.059
|
| HMC_vs_Metro |
2
|
-9.259
|
3.67e-10
|
-1.690
|
| HMC_vs_Metro |
3
|
-21.815
|
1.54e-19
|
-3.983
|
| HMC_vs_Metro |
4
|
-21.476
|
2.36e-19
|
-3.921
|
| HMC_vs_SMC |
0
|
-22.431
|
7.17e-20
|
-4.095
|
| HMC_vs_SMC |
1
|
-27.191
|
3.46e-22
|
-4.964
|
| HMC_vs_SMC |
2
|
-21.972
|
1.26e-19
|
-4.012
|
| HMC_vs_SMC |
3
|
-26.827
|
5.04e-22
|
-4.898
|
| HMC_vs_SMC |
4
|
-23.124
|
3.1e-20
|
-4.222
|
| DEMetro_Z_vs_SMC |
0
|
15.742
|
9.6e-16
|
2.874
|
| DEMetro_Z_vs_SMC |
1
|
14.131
|
1.55e-14
|
2.580
|
| DEMetro_Z_vs_SMC |
2
|
15.809
|
8.6e-16
|
2.886
|
| DEMetro_Z_vs_SMC |
3
|
10.853
|
9.98e-12
|
1.981
|
| DEMetro_Z_vs_SMC |
4
|
10.023
|
6.27e-11
|
1.830
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.136 |
0.070 |
0.022 |
2.965 |
| HMC |
3.0 |
0.041 |
0.038 |
0.005 |
0.438 |
| HMC |
4.0 |
0.031 |
0.032 |
0.004 |
-0.272 |
| HMC |
10.0 |
0.022 |
0.024 |
0.003 |
-0.713 |
| HMC |
50.0 |
0.020 |
0.022 |
0.003 |
-0.876 |
| SMC |
2.1 |
1.418 |
0.070 |
0.022 |
60.674 |
| SMC |
3.0 |
0.397 |
0.038 |
0.005 |
65.762 |
| SMC |
4.0 |
0.304 |
0.032 |
0.004 |
70.823 |
| SMC |
10.0 |
0.173 |
0.024 |
0.003 |
45.541 |
| SMC |
50.0 |
0.073 |
0.022 |
0.003 |
17.937 |
| Metro |
2.1 |
0.264 |
0.070 |
0.022 |
8.726 |
| Metro |
3.0 |
0.077 |
0.038 |
0.005 |
7.150 |
| Metro |
4.0 |
0.065 |
0.032 |
0.004 |
8.657 |
| Metro |
10.0 |
0.051 |
0.024 |
0.003 |
8.097 |
| Metro |
50.0 |
0.041 |
0.022 |
0.003 |
6.617 |
| DEMetro_Z |
2.1 |
7.785 |
0.070 |
0.022 |
347.184 |
| DEMetro_Z |
3.0 |
1.998 |
0.038 |
0.005 |
359.552 |
| DEMetro_Z |
4.0 |
1.603 |
0.032 |
0.004 |
409.903 |
| DEMetro_Z |
10.0 |
1.021 |
0.024 |
0.003 |
304.126 |
| DEMetro_Z |
50.0 |
0.618 |
0.022 |
0.003 |
209.480 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
0.632 |
0.532 |
0.404 |
| HMC |
3.0 |
0.034 |
0.973 |
0.007 |
| HMC |
4.0 |
2.044 |
0.0466 |
0.733 |
| HMC |
10.0 |
7.651 |
8.55e-10 |
2.754 |
| HMC |
50.0 |
10.548 |
9.46e-15 |
3.172 |
| SMC |
2.1 |
101.305 |
2.3e-39 |
160.489 |
| SMC |
3.0 |
158.780 |
6.81e-45 |
295.664 |
| SMC |
4.0 |
100.962 |
1.67e-38 |
1407.573 |
| SMC |
10.0 |
79.775 |
1.55e-35 |
11879.703 |
| SMC |
50.0 |
28.757 |
7.21e-23 |
1396.367 |
| Metro |
2.1 |
1.616 |
0.116 |
1.081 |
| Metro |
3.0 |
0.328 |
0.745 |
0.067 |
| Metro |
4.0 |
3.183 |
0.00324 |
2.618 |
| Metro |
10.0 |
13.293 |
7.28e-15 |
9.241 |
| Metro |
50.0 |
20.346 |
9.8e-23 |
9.126 |
| DEMetro_Z |
2.1 |
10.240 |
3.36e-11 |
24.122 |
| DEMetro_Z |
3.0 |
7.574 |
2.29e-08 |
24.815 |
| DEMetro_Z |
4.0 |
9.416 |
2.53e-10 |
112.138 |
| DEMetro_Z |
10.0 |
5.369 |
9.11e-06 |
630.386 |
| DEMetro_Z |
50.0 |
3.352 |
0.00225 |
396.386 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
-90.220
|
4.43e-37
|
-16.472
|
| HMC_vs_SMC |
1
|
-160.399
|
2.59e-44
|
-29.285
|
| HMC_vs_SMC |
2
|
-101.243
|
1.58e-38
|
-18.484
|
| HMC_vs_SMC |
3
|
-79.774
|
1.55e-35
|
-14.565
|
| HMC_vs_SMC |
4
|
-28.664
|
7.9e-23
|
-5.233
|
| Metro_vs_DEMetro_Z |
0
|
-9.116
|
5.16e-10
|
-1.664
|
| Metro_vs_DEMetro_Z |
1
|
-7.569
|
2.41e-08
|
-1.382
|
| Metro_vs_DEMetro_Z |
2
|
-9.042
|
6.15e-10
|
-1.651
|
| Metro_vs_DEMetro_Z |
3
|
-5.285
|
1.15e-05
|
-0.965
|
| Metro_vs_DEMetro_Z |
4
|
-3.277
|
0.00272
|
-0.598
|
| HMC_vs_Metro |
0
|
-0.734
|
0.469
|
-0.134
|
| HMC_vs_Metro |
1
|
-0.387
|
0.702
|
-0.071
|
| HMC_vs_Metro |
2
|
-2.138
|
0.0411
|
-0.390
|
| HMC_vs_Metro |
3
|
-10.597
|
1.74e-11
|
-1.935
|
| HMC_vs_Metro |
4
|
-13.603
|
4.07e-14
|
-2.484
|
| HMC_vs_DEMetro_Z |
0
|
-10.841
|
1.02e-11
|
-1.979
|
| HMC_vs_DEMetro_Z |
1
|
-7.540
|
2.6e-08
|
-1.377
|
| HMC_vs_DEMetro_Z |
2
|
-9.361
|
2.89e-10
|
-1.709
|
| HMC_vs_DEMetro_Z |
3
|
-5.342
|
9.8e-06
|
-0.975
|
| HMC_vs_DEMetro_Z |
4
|
-3.326
|
0.0024
|
-0.607
|
| Metro_vs_SMC |
0
|
-85.623
|
2.01e-36
|
-15.633
|
| Metro_vs_SMC |
1
|
-157.415
|
4.47e-44
|
-28.740
|
| Metro_vs_SMC |
2
|
-100.771
|
1.81e-38
|
-18.398
|
| Metro_vs_SMC |
3
|
-79.720
|
1.58e-35
|
-14.555
|
| Metro_vs_SMC |
4
|
-28.585
|
8.53e-23
|
-5.219
|
| DEMetro_Z_vs_SMC |
0
|
-47.755
|
4.01e-29
|
-8.719
|
| DEMetro_Z_vs_SMC |
1
|
-63.609
|
1.06e-32
|
-11.613
|
| DEMetro_Z_vs_SMC |
2
|
-65.744
|
4.1e-33
|
-12.003
|
| DEMetro_Z_vs_SMC |
3
|
-52.722
|
2.35e-30
|
-9.626
|
| DEMetro_Z_vs_SMC |
4
|
-7.897
|
1.04e-08
|
-1.442
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
16.673 |
9.489 |
17.780 |
0.404 |
| HMC |
3.0 |
0.756 |
0.749 |
0.992 |
0.007 |
| HMC |
4.0 |
0.284 |
0.190 |
0.128 |
0.733 |
| HMC |
10.0 |
0.068 |
0.050 |
0.007 |
2.754 |
| HMC |
50.0 |
0.045 |
0.033 |
0.004 |
3.172 |
| SMC |
2.1 |
2862.923 |
9.489 |
17.780 |
160.489 |
| SMC |
3.0 |
294.010 |
0.749 |
0.992 |
295.664 |
| SMC |
4.0 |
180.246 |
0.190 |
0.128 |
1407.573 |
| SMC |
10.0 |
80.428 |
0.050 |
0.007 |
11879.703 |
| SMC |
50.0 |
5.419 |
0.033 |
0.004 |
1396.367 |
| Metro |
2.1 |
28.707 |
9.489 |
17.780 |
1.081 |
| Metro |
3.0 |
0.815 |
0.749 |
0.992 |
0.067 |
| Metro |
4.0 |
0.525 |
0.190 |
0.128 |
2.618 |
| Metro |
10.0 |
0.112 |
0.050 |
0.007 |
9.241 |
| Metro |
50.0 |
0.068 |
0.033 |
0.004 |
9.126 |
| DEMetro_Z |
2.1 |
438.374 |
9.489 |
17.780 |
24.122 |
| DEMetro_Z |
3.0 |
25.362 |
0.749 |
0.992 |
24.815 |
| DEMetro_Z |
4.0 |
14.535 |
0.190 |
0.128 |
112.138 |
| DEMetro_Z |
10.0 |
4.315 |
0.050 |
0.007 |
630.386 |
| DEMetro_Z |
50.0 |
1.562 |
0.033 |
0.004 |
396.386 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
1.663 |
0.107 |
19.157 |
| HMC |
3.0 |
3.991 |
0.000401 |
8.462 |
| HMC |
4.0 |
2.547 |
0.0163 |
5.306 |
| HMC |
10.0 |
3.284 |
0.00178 |
0.967 |
| HMC |
50.0 |
1.489 |
0.142 |
0.335 |
| SMC |
2.1 |
192.736 |
1.13e-46 |
1406.790 |
| SMC |
3.0 |
277.240 |
3.05e-51 |
2282.622 |
| SMC |
4.0 |
175.319 |
1.93e-45 |
2731.355 |
| SMC |
10.0 |
141.941 |
8.87e-43 |
3454.406 |
| SMC |
50.0 |
41.743 |
1.86e-27 |
780.220 |
| Metro |
2.1 |
4.000 |
0.000399 |
30.843 |
| Metro |
3.0 |
7.581 |
2.11e-08 |
15.683 |
| Metro |
4.0 |
7.585 |
2.11e-08 |
16.605 |
| Metro |
10.0 |
20.648 |
1.08e-20 |
13.765 |
| Metro |
50.0 |
21.887 |
4.82e-24 |
9.666 |
| DEMetro_Z |
2.1 |
19.490 |
3.29e-18 |
511.010 |
| DEMetro_Z |
3.0 |
14.741 |
5.26e-15 |
534.318 |
| DEMetro_Z |
4.0 |
17.332 |
7.63e-17 |
615.004 |
| DEMetro_Z |
10.0 |
13.177 |
9.03e-14 |
631.076 |
| DEMetro_Z |
50.0 |
10.597 |
1.74e-11 |
384.139 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-17.842
|
3.53e-17
|
-3.258
|
| Metro_vs_DEMetro_Z |
1
|
-14.248
|
1.26e-14
|
-2.601
|
| Metro_vs_DEMetro_Z |
2
|
-16.623
|
2.31e-16
|
-3.035
|
| Metro_vs_DEMetro_Z |
3
|
-12.855
|
1.67e-13
|
-2.347
|
| Metro_vs_DEMetro_Z |
4
|
-10.382
|
2.8e-11
|
-1.895
|
| DEMetro_Z_vs_SMC |
0
|
-32.867
|
1.68e-24
|
-6.001
|
| DEMetro_Z_vs_SMC |
1
|
-43.824
|
4.68e-28
|
-8.001
|
| DEMetro_Z_vs_SMC |
2
|
-51.540
|
4.5e-30
|
-9.410
|
| DEMetro_Z_vs_SMC |
3
|
-49.972
|
1.09e-29
|
-9.124
|
| DEMetro_Z_vs_SMC |
4
|
-9.418
|
2.52e-10
|
-1.720
|
| HMC_vs_DEMetro_Z |
0
|
-20.137
|
1.36e-18
|
-3.677
|
| HMC_vs_DEMetro_Z |
1
|
-14.523
|
7.71e-15
|
-2.651
|
| HMC_vs_DEMetro_Z |
2
|
-17.211
|
9.2e-17
|
-3.142
|
| HMC_vs_DEMetro_Z |
3
|
-13.163
|
9.28e-14
|
-2.403
|
| HMC_vs_DEMetro_Z |
4
|
-10.604
|
1.72e-11
|
-1.936
|
| HMC_vs_Metro |
0
|
-0.807
|
0.426
|
-0.147
|
| HMC_vs_Metro |
1
|
-2.253
|
0.032
|
-0.411
|
| HMC_vs_Metro |
2
|
-3.501
|
0.00152
|
-0.639
|
| HMC_vs_Metro |
3
|
-19.847
|
2.02e-18
|
-3.624
|
| HMC_vs_Metro |
4
|
-24.627
|
5.45e-21
|
-4.496
|
| HMC_vs_SMC |
0
|
-94.981
|
1e-37
|
-17.341
|
| HMC_vs_SMC |
1
|
-270.919
|
6.56e-51
|
-49.463
|
| HMC_vs_SMC |
2
|
-174.554
|
2.24e-45
|
-31.869
|
| HMC_vs_SMC |
3
|
-142.207
|
8.48e-43
|
-25.963
|
| HMC_vs_SMC |
4
|
-41.654
|
2e-27
|
-7.605
|
| Metro_vs_SMC |
0
|
-115.966
|
3.11e-40
|
-21.172
|
| Metro_vs_SMC |
1
|
-248.197
|
8.31e-50
|
-45.314
|
| Metro_vs_SMC |
2
|
-175.569
|
1.89e-45
|
-32.054
|
| Metro_vs_SMC |
3
|
-141.126
|
1.06e-42
|
-25.766
|
| Metro_vs_SMC |
4
|
-40.900
|
3.37e-27
|
-7.467
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.677 |
0.118 |
0.029 |
19.157 |
| HMC |
3.0 |
0.112 |
0.065 |
0.005 |
8.462 |
| HMC |
4.0 |
0.068 |
0.050 |
0.004 |
5.306 |
| HMC |
10.0 |
0.035 |
0.034 |
0.002 |
0.967 |
| HMC |
50.0 |
0.030 |
0.029 |
0.002 |
0.335 |
| SMC |
2.1 |
41.159 |
0.118 |
0.029 |
1406.790 |
| SMC |
3.0 |
12.612 |
0.065 |
0.005 |
2282.622 |
| SMC |
4.0 |
9.742 |
0.050 |
0.004 |
2731.355 |
| SMC |
10.0 |
6.340 |
0.034 |
0.002 |
3454.406 |
| SMC |
50.0 |
1.222 |
0.029 |
0.002 |
780.220 |
| Metro |
2.1 |
1.018 |
0.118 |
0.029 |
30.843 |
| Metro |
3.0 |
0.151 |
0.065 |
0.005 |
15.683 |
| Metro |
4.0 |
0.108 |
0.050 |
0.004 |
16.605 |
| Metro |
10.0 |
0.059 |
0.034 |
0.002 |
13.765 |
| Metro |
50.0 |
0.044 |
0.029 |
0.002 |
9.666 |
| DEMetro_Z |
2.1 |
15.026 |
0.118 |
0.029 |
511.010 |
| DEMetro_Z |
3.0 |
3.002 |
0.065 |
0.005 |
534.318 |
| DEMetro_Z |
4.0 |
2.232 |
0.050 |
0.004 |
615.004 |
| DEMetro_Z |
10.0 |
1.186 |
0.034 |
0.002 |
631.076 |
| DEMetro_Z |
50.0 |
0.616 |
0.029 |
0.002 |
384.139 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
3.242 |
0.00298 |
43.840 |
| HMC |
3.0 |
4.050 |
0.000343 |
9.114 |
| HMC |
4.0 |
2.718 |
0.0109 |
5.311 |
| HMC |
10.0 |
1.333 |
0.188 |
0.400 |
| HMC |
50.0 |
0.228 |
0.821 |
0.051 |
| SMC |
2.1 |
181.443 |
4.72e-47 |
267.347 |
| SMC |
3.0 |
257.151 |
3.02e-53 |
254.053 |
| SMC |
4.0 |
179.074 |
1.08e-46 |
287.756 |
| SMC |
10.0 |
204.776 |
6.13e-49 |
269.607 |
| SMC |
50.0 |
86.892 |
5.87e-37 |
204.820 |
| Metro |
2.1 |
7.851 |
1.17e-08 |
85.605 |
| Metro |
3.0 |
7.435 |
3.24e-08 |
20.963 |
| Metro |
4.0 |
10.049 |
4.52e-11 |
16.601 |
| Metro |
10.0 |
19.333 |
8.57e-21 |
10.300 |
| Metro |
50.0 |
19.950 |
1.25e-23 |
7.834 |
| DEMetro_Z |
2.1 |
52.346 |
2.66e-30 |
345.566 |
| DEMetro_Z |
3.0 |
45.455 |
1.52e-28 |
288.070 |
| DEMetro_Z |
4.0 |
41.322 |
2.39e-27 |
319.010 |
| DEMetro_Z |
10.0 |
24.657 |
5.17e-21 |
269.336 |
| DEMetro_Z |
50.0 |
18.241 |
1.93e-17 |
201.757 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
11.286
|
3.96e-12
|
2.061
|
| DEMetro_Z_vs_SMC |
1
|
5.468
|
6.91e-06
|
0.998
|
| DEMetro_Z_vs_SMC |
2
|
4.053
|
0.000347
|
0.740
|
| DEMetro_Z_vs_SMC |
3
|
-0.024
|
0.981
|
-0.004
|
| DEMetro_Z_vs_SMC |
4
|
-0.253
|
0.802
|
-0.046
|
| HMC_vs_Metro |
0
|
-2.598
|
0.0146
|
-0.474
|
| HMC_vs_Metro |
1
|
-3.004
|
0.00545
|
-0.548
|
| HMC_vs_Metro |
2
|
-4.130
|
0.000281
|
-0.754
|
| HMC_vs_Metro |
3
|
-19.468
|
3.4e-18
|
-3.554
|
| HMC_vs_Metro |
4
|
-22.279
|
8.64e-20
|
-4.068
|
| Metro_vs_DEMetro_Z |
0
|
-22.103
|
1.07e-19
|
-4.035
|
| Metro_vs_DEMetro_Z |
1
|
-35.713
|
1.6e-25
|
-6.520
|
| Metro_vs_DEMetro_Z |
2
|
-37.715
|
3.39e-26
|
-6.886
|
| Metro_vs_DEMetro_Z |
3
|
-23.560
|
1.85e-20
|
-4.302
|
| Metro_vs_DEMetro_Z |
4
|
-17.823
|
3.64e-17
|
-3.254
|
| HMC_vs_SMC |
0
|
-16.770
|
1.83e-16
|
-3.062
|
| HMC_vs_SMC |
1
|
-104.149
|
6.97e-39
|
-19.015
|
| HMC_vs_SMC |
2
|
-116.122
|
2.99e-40
|
-21.201
|
| HMC_vs_SMC |
3
|
-199.603
|
4.6e-47
|
-36.442
|
| HMC_vs_SMC |
4
|
-86.161
|
1.67e-36
|
-15.731
|
| Metro_vs_SMC |
0
|
-17.112
|
1.07e-16
|
-3.124
|
| Metro_vs_SMC |
1
|
-81.448
|
8.51e-36
|
-14.870
|
| Metro_vs_SMC |
2
|
-124.690
|
3.81e-41
|
-22.765
|
| Metro_vs_SMC |
3
|
-181.571
|
7.15e-46
|
-33.150
|
| Metro_vs_SMC |
4
|
-79.288
|
1.85e-35
|
-14.476
|
| HMC_vs_DEMetro_Z |
0
|
-21.037
|
4.15e-19
|
-3.841
|
| HMC_vs_DEMetro_Z |
1
|
-45.373
|
1.73e-28
|
-8.284
|
| HMC_vs_DEMetro_Z |
2
|
-47.618
|
4.36e-29
|
-8.694
|
| HMC_vs_DEMetro_Z |
3
|
-24.650
|
5.31e-21
|
-4.500
|
| HMC_vs_DEMetro_Z |
4
|
-18.278
|
1.85e-17
|
-3.337
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.081 |
0.015 |
0.001 |
43.840 |
| HMC |
3.0 |
0.029 |
0.015 |
0.002 |
9.114 |
| HMC |
4.0 |
0.022 |
0.015 |
0.001 |
5.311 |
| HMC |
10.0 |
0.015 |
0.014 |
0.001 |
0.400 |
| HMC |
50.0 |
0.014 |
0.014 |
0.001 |
0.051 |
| SMC |
2.1 |
0.416 |
0.015 |
0.001 |
267.347 |
| SMC |
3.0 |
0.408 |
0.015 |
0.002 |
254.053 |
| SMC |
4.0 |
0.406 |
0.015 |
0.001 |
287.756 |
| SMC |
10.0 |
0.402 |
0.014 |
0.001 |
269.607 |
| SMC |
50.0 |
0.289 |
0.014 |
0.001 |
204.820 |
| Metro |
2.1 |
0.143 |
0.015 |
0.001 |
85.605 |
| Metro |
3.0 |
0.048 |
0.015 |
0.002 |
20.963 |
| Metro |
4.0 |
0.037 |
0.015 |
0.001 |
16.601 |
| Metro |
10.0 |
0.029 |
0.014 |
0.001 |
10.300 |
| Metro |
50.0 |
0.024 |
0.014 |
0.001 |
7.834 |
| DEMetro_Z |
2.1 |
0.533 |
0.015 |
0.001 |
345.566 |
| DEMetro_Z |
3.0 |
0.460 |
0.015 |
0.002 |
288.070 |
| DEMetro_Z |
4.0 |
0.448 |
0.015 |
0.001 |
319.010 |
| DEMetro_Z |
10.0 |
0.402 |
0.014 |
0.001 |
269.336 |
| DEMetro_Z |
50.0 |
0.284 |
0.014 |
0.001 |
201.757 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
Trace Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Varying_Tails_with_high_Correlation
(MvStudentT,
nu,
30 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
1.462 |
0.15 |
0.456 |
| HMC |
3.0 |
4.335 |
8.6e-05 |
1.743 |
| HMC |
4.0 |
3.908 |
0.000399 |
2.216 |
| HMC |
10.0 |
3.901 |
0.000305 |
1.410 |
| HMC |
50.0 |
2.173 |
0.0349 |
0.801 |
| SMC |
2.1 |
2.392 |
0.0215 |
1.052 |
| SMC |
3.0 |
1.144 |
0.258 |
0.350 |
| SMC |
4.0 |
1.838 |
0.0718 |
0.582 |
| SMC |
10.0 |
-0.910 |
0.367 |
-0.213 |
| SMC |
50.0 |
-0.313 |
0.755 |
-0.082 |
| Metro |
2.1 |
5.171 |
8.64e-06 |
2.781 |
| Metro |
3.0 |
5.553 |
5.24e-06 |
13.031 |
| Metro |
4.0 |
6.272 |
6.8e-07 |
10.262 |
| Metro |
10.0 |
6.410 |
3.94e-07 |
6.695 |
| Metro |
50.0 |
5.628 |
3.21e-06 |
4.663 |
| DEMetro_Z |
2.1 |
3.481 |
0.00111 |
1.285 |
| DEMetro_Z |
3.0 |
4.813 |
3.53e-05 |
4.259 |
| DEMetro_Z |
4.0 |
4.420 |
9.24e-05 |
2.680 |
| DEMetro_Z |
10.0 |
3.449 |
0.00144 |
1.861 |
| DEMetro_Z |
50.0 |
2.223 |
0.0314 |
0.883 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-2.021
|
0.0525
|
-0.369
|
| HMC_vs_DEMetro_Z |
1
|
-2.773
|
0.00962
|
-0.506
|
| HMC_vs_DEMetro_Z |
2
|
-0.615
|
0.543
|
-0.112
|
| HMC_vs_DEMetro_Z |
3
|
-0.869
|
0.392
|
-0.159
|
| HMC_vs_DEMetro_Z |
4
|
-0.171
|
0.865
|
-0.031
|
| Metro_vs_SMC |
0
|
2.307
|
0.0284
|
0.421
|
| Metro_vs_SMC |
1
|
5.309
|
1.07e-05
|
0.969
|
| Metro_vs_SMC |
2
|
6.016
|
1.52e-06
|
1.098
|
| Metro_vs_SMC |
3
|
6.741
|
2.13e-07
|
1.231
|
| Metro_vs_SMC |
4
|
6.443
|
4.76e-07
|
1.176
|
| Metro_vs_DEMetro_Z |
0
|
2.565
|
0.0158
|
0.468
|
| Metro_vs_DEMetro_Z |
1
|
3.864
|
0.000577
|
0.706
|
| Metro_vs_DEMetro_Z |
2
|
4.204
|
0.00023
|
0.767
|
| Metro_vs_DEMetro_Z |
3
|
3.911
|
0.000509
|
0.714
|
| Metro_vs_DEMetro_Z |
4
|
4.497
|
0.000102
|
0.821
|
| HMC_vs_Metro |
0
|
-4.529
|
9.38e-05
|
-0.827
|
| HMC_vs_Metro |
1
|
-4.685
|
6.09e-05
|
-0.855
|
| HMC_vs_Metro |
2
|
-4.537
|
9.17e-05
|
-0.828
|
| HMC_vs_Metro |
3
|
-5.160
|
1.63e-05
|
-0.942
|
| HMC_vs_Metro |
4
|
-4.209
|
0.000226
|
-0.769
|
| HMC_vs_SMC |
0
|
-1.240
|
0.225
|
-0.226
|
| HMC_vs_SMC |
1
|
2.940
|
0.00638
|
0.537
|
| HMC_vs_SMC |
2
|
2.627
|
0.0136
|
0.480
|
| HMC_vs_SMC |
3
|
5.238
|
1.31e-05
|
0.956
|
| HMC_vs_SMC |
4
|
2.546
|
0.0165
|
0.465
|
| DEMetro_Z_vs_SMC |
0
|
0.471
|
0.641
|
0.086
|
| DEMetro_Z_vs_SMC |
1
|
4.339
|
0.000158
|
0.792
|
| DEMetro_Z_vs_SMC |
2
|
3.552
|
0.00133
|
0.649
|
| DEMetro_Z_vs_SMC |
3
|
3.856
|
0.00059
|
0.704
|
| DEMetro_Z_vs_SMC |
4
|
3.055
|
0.0048
|
0.558
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.082 |
0.062 |
0.044 |
0.456 |
| HMC |
3.0 |
0.055 |
0.027 |
0.016 |
1.743 |
| HMC |
4.0 |
0.050 |
0.022 |
0.013 |
2.216 |
| HMC |
10.0 |
0.036 |
0.019 |
0.013 |
1.410 |
| HMC |
50.0 |
0.030 |
0.021 |
0.012 |
0.801 |
| SMC |
2.1 |
0.109 |
0.062 |
0.044 |
1.052 |
| SMC |
3.0 |
0.033 |
0.027 |
0.016 |
0.350 |
| SMC |
4.0 |
0.029 |
0.022 |
0.013 |
0.582 |
| SMC |
10.0 |
0.016 |
0.019 |
0.013 |
-0.213 |
| SMC |
50.0 |
0.020 |
0.021 |
0.012 |
-0.082 |
| Metro |
2.1 |
0.184 |
0.062 |
0.044 |
2.781 |
| Metro |
3.0 |
0.233 |
0.027 |
0.016 |
13.031 |
| Metro |
4.0 |
0.152 |
0.022 |
0.013 |
10.262 |
| Metro |
10.0 |
0.103 |
0.019 |
0.013 |
6.695 |
| Metro |
50.0 |
0.077 |
0.021 |
0.012 |
4.663 |
| DEMetro_Z |
2.1 |
0.119 |
0.062 |
0.044 |
1.285 |
| DEMetro_Z |
3.0 |
0.094 |
0.027 |
0.016 |
4.259 |
| DEMetro_Z |
4.0 |
0.056 |
0.022 |
0.013 |
2.680 |
| DEMetro_Z |
10.0 |
0.042 |
0.019 |
0.013 |
1.861 |
| DEMetro_Z |
50.0 |
0.031 |
0.021 |
0.012 |
0.883 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
-1.260 |
0.216 |
-0.245 |
| HMC |
3.0 |
2.051 |
0.0459 |
0.736 |
| HMC |
4.0 |
1.508 |
0.139 |
0.670 |
| HMC |
10.0 |
2.302 |
0.026 |
0.876 |
| HMC |
50.0 |
3.380 |
0.00152 |
1.301 |
| SMC |
2.1 |
2.547 |
0.0143 |
0.536 |
| SMC |
3.0 |
3.260 |
0.00206 |
1.149 |
| SMC |
4.0 |
-0.529 |
0.599 |
-0.149 |
| SMC |
10.0 |
-0.025 |
0.98 |
-0.007 |
| SMC |
50.0 |
-1.300 |
0.199 |
-0.343 |
| Metro |
2.1 |
-1.233 |
0.226 |
-0.234 |
| Metro |
3.0 |
2.490 |
0.0186 |
3.985 |
| Metro |
4.0 |
2.416 |
0.0222 |
6.658 |
| Metro |
10.0 |
5.160 |
1.12e-05 |
3.540 |
| Metro |
50.0 |
6.170 |
6.5e-07 |
4.948 |
| DEMetro_Z |
2.1 |
-1.590 |
0.122 |
-0.297 |
| DEMetro_Z |
3.0 |
3.918 |
0.000267 |
1.279 |
| DEMetro_Z |
4.0 |
3.274 |
0.00209 |
1.307 |
| DEMetro_Z |
10.0 |
4.425 |
7.59e-05 |
2.095 |
| DEMetro_Z |
50.0 |
4.154 |
0.00013 |
1.415 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
-5.445
|
7.38e-06
|
-0.994
|
| HMC_vs_SMC |
1
|
-1.130
|
0.268
|
-0.206
|
| HMC_vs_SMC |
2
|
1.855
|
0.0738
|
0.339
|
| HMC_vs_SMC |
3
|
2.024
|
0.0523
|
0.370
|
| HMC_vs_SMC |
4
|
3.859
|
0.000586
|
0.705
|
| Metro_vs_DEMetro_Z |
0
|
1.877
|
0.0706
|
0.343
|
| Metro_vs_DEMetro_Z |
1
|
1.850
|
0.0745
|
0.338
|
| Metro_vs_DEMetro_Z |
2
|
1.954
|
0.0604
|
0.357
|
| Metro_vs_DEMetro_Z |
3
|
1.754
|
0.09
|
0.320
|
| Metro_vs_DEMetro_Z |
4
|
3.946
|
0.000463
|
0.721
|
| HMC_vs_Metro |
0
|
-0.180
|
0.858
|
-0.033
|
| HMC_vs_Metro |
1
|
-1.941
|
0.0621
|
-0.354
|
| HMC_vs_Metro |
2
|
-2.185
|
0.0371
|
-0.399
|
| HMC_vs_Metro |
3
|
-3.673
|
0.000963
|
-0.671
|
| HMC_vs_Metro |
4
|
-4.475
|
0.000109
|
-0.817
|
| HMC_vs_DEMetro_Z |
0
|
0.859
|
0.397
|
0.157
|
| HMC_vs_DEMetro_Z |
1
|
-1.344
|
0.189
|
-0.245
|
| HMC_vs_DEMetro_Z |
2
|
-1.139
|
0.264
|
-0.208
|
| HMC_vs_DEMetro_Z |
3
|
-2.270
|
0.0308
|
-0.415
|
| HMC_vs_DEMetro_Z |
4
|
-0.247
|
0.807
|
-0.045
|
| Metro_vs_SMC |
0
|
-6.009
|
1.56e-06
|
-1.097
|
| Metro_vs_SMC |
1
|
1.682
|
0.103
|
0.307
|
| Metro_vs_SMC |
2
|
2.428
|
0.0216
|
0.443
|
| Metro_vs_SMC |
3
|
5.257
|
1.24e-05
|
0.960
|
| Metro_vs_SMC |
4
|
6.438
|
4.82e-07
|
1.175
|
| DEMetro_Z_vs_SMC |
0
|
-6.841
|
1.63e-07
|
-1.249
|
| DEMetro_Z_vs_SMC |
1
|
0.321
|
0.75
|
0.059
|
| DEMetro_Z_vs_SMC |
2
|
3.887
|
0.000543
|
0.710
|
| DEMetro_Z_vs_SMC |
3
|
4.296
|
0.000178
|
0.784
|
| DEMetro_Z_vs_SMC |
4
|
5.445
|
7.37e-06
|
0.994
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
4.381 |
7.895 |
14.317 |
-0.245 |
| HMC |
3.0 |
0.614 |
0.368 |
0.335 |
0.736 |
| HMC |
4.0 |
0.206 |
0.147 |
0.088 |
0.670 |
| HMC |
10.0 |
0.069 |
0.045 |
0.027 |
0.876 |
| HMC |
50.0 |
0.049 |
0.028 |
0.016 |
1.301 |
| SMC |
2.1 |
15.567 |
7.895 |
14.317 |
0.536 |
| SMC |
3.0 |
0.753 |
0.368 |
0.335 |
1.149 |
| SMC |
4.0 |
0.134 |
0.147 |
0.088 |
-0.149 |
| SMC |
10.0 |
0.045 |
0.045 |
0.027 |
-0.007 |
| SMC |
50.0 |
0.023 |
0.028 |
0.016 |
-0.343 |
| Metro |
2.1 |
4.542 |
7.895 |
14.317 |
-0.234 |
| Metro |
3.0 |
1.701 |
0.368 |
0.335 |
3.985 |
| Metro |
4.0 |
0.731 |
0.147 |
0.088 |
6.658 |
| Metro |
10.0 |
0.141 |
0.045 |
0.027 |
3.540 |
| Metro |
50.0 |
0.106 |
0.028 |
0.016 |
4.948 |
| DEMetro_Z |
2.1 |
3.646 |
7.895 |
14.317 |
-0.297 |
| DEMetro_Z |
3.0 |
0.796 |
0.368 |
0.335 |
1.279 |
| DEMetro_Z |
4.0 |
0.261 |
0.147 |
0.088 |
1.307 |
| DEMetro_Z |
10.0 |
0.102 |
0.045 |
0.027 |
2.095 |
| DEMetro_Z |
50.0 |
0.051 |
0.028 |
0.016 |
1.415 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
2.652 |
0.011 |
0.994 |
| HMC |
3.0 |
6.850 |
3.09e-08 |
3.100 |
| HMC |
4.0 |
5.684 |
2.19e-06 |
3.629 |
| HMC |
10.0 |
4.818 |
2.06e-05 |
2.129 |
| HMC |
50.0 |
3.889 |
0.000308 |
1.357 |
| SMC |
2.1 |
12.165 |
4.57e-13 |
20.206 |
| SMC |
3.0 |
4.407 |
0.000112 |
3.788 |
| SMC |
4.0 |
1.024 |
0.31 |
0.316 |
| SMC |
10.0 |
0.230 |
0.819 |
0.060 |
| SMC |
50.0 |
-0.581 |
0.563 |
-0.143 |
| Metro |
2.1 |
10.670 |
4.49e-13 |
5.107 |
| Metro |
3.0 |
7.072 |
8.44e-08 |
20.043 |
| Metro |
4.0 |
7.982 |
7.7e-09 |
18.835 |
| Metro |
10.0 |
7.917 |
7.5e-09 |
10.357 |
| Metro |
50.0 |
6.731 |
1.55e-07 |
6.646 |
| DEMetro_Z |
2.1 |
7.363 |
6.52e-09 |
3.413 |
| DEMetro_Z |
3.0 |
9.230 |
1.87e-10 |
8.499 |
| DEMetro_Z |
4.0 |
10.589 |
1.04e-12 |
5.602 |
| DEMetro_Z |
10.0 |
7.465 |
8.41e-09 |
4.177 |
| DEMetro_Z |
50.0 |
5.400 |
2.16e-06 |
1.947 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
3.783
|
0.000719
|
0.691
|
| Metro_vs_DEMetro_Z |
1
|
4.293
|
0.000179
|
0.784
|
| Metro_vs_DEMetro_Z |
2
|
5.409
|
8.15e-06
|
0.987
|
| Metro_vs_DEMetro_Z |
3
|
4.274
|
0.000189
|
0.780
|
| Metro_vs_DEMetro_Z |
4
|
4.775
|
4.74e-05
|
0.872
|
| DEMetro_Z_vs_SMC |
0
|
-9.658
|
1.44e-10
|
-1.763
|
| DEMetro_Z_vs_SMC |
1
|
3.741
|
0.000804
|
0.683
|
| DEMetro_Z_vs_SMC |
2
|
9.185
|
4.38e-10
|
1.677
|
| DEMetro_Z_vs_SMC |
3
|
7.691
|
1.76e-08
|
1.404
|
| DEMetro_Z_vs_SMC |
4
|
7.623
|
2.1e-08
|
1.392
|
| HMC_vs_DEMetro_Z |
0
|
-4.430
|
0.000123
|
-0.809
|
| HMC_vs_DEMetro_Z |
1
|
-5.681
|
3.84e-06
|
-1.037
|
| HMC_vs_DEMetro_Z |
2
|
-2.575
|
0.0154
|
-0.470
|
| HMC_vs_DEMetro_Z |
3
|
-3.664
|
0.000988
|
-0.669
|
| HMC_vs_DEMetro_Z |
4
|
-1.243
|
0.224
|
-0.227
|
| HMC_vs_Metro |
0
|
-7.335
|
4.43e-08
|
-1.339
|
| HMC_vs_Metro |
1
|
-5.787
|
2.86e-06
|
-1.057
|
| HMC_vs_Metro |
2
|
-6.274
|
7.54e-07
|
-1.145
|
| HMC_vs_Metro |
3
|
-6.290
|
7.22e-07
|
-1.148
|
| HMC_vs_Metro |
4
|
-4.924
|
3.13e-05
|
-0.899
|
| HMC_vs_SMC |
0
|
-11.051
|
6.53e-12
|
-2.018
|
| HMC_vs_SMC |
1
|
-0.740
|
0.465
|
-0.135
|
| HMC_vs_SMC |
2
|
4.549
|
8.87e-05
|
0.831
|
| HMC_vs_SMC |
3
|
4.477
|
0.000108
|
0.817
|
| HMC_vs_SMC |
4
|
4.530
|
9.35e-05
|
0.827
|
| Metro_vs_SMC |
0
|
-8.527
|
2.15e-09
|
-1.557
|
| Metro_vs_SMC |
1
|
5.456
|
7.15e-06
|
0.996
|
| Metro_vs_SMC |
2
|
7.820
|
1.27e-08
|
1.428
|
| Metro_vs_SMC |
3
|
7.817
|
1.27e-08
|
1.427
|
| Metro_vs_SMC |
4
|
7.381
|
3.93e-08
|
1.348
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.157 |
0.118 |
0.039 |
0.994 |
| HMC |
3.0 |
0.091 |
0.060 |
0.010 |
3.100 |
| HMC |
4.0 |
0.072 |
0.043 |
0.008 |
3.629 |
| HMC |
10.0 |
0.048 |
0.031 |
0.008 |
2.129 |
| HMC |
50.0 |
0.041 |
0.029 |
0.008 |
1.357 |
| SMC |
2.1 |
0.914 |
0.118 |
0.039 |
20.206 |
| SMC |
3.0 |
0.099 |
0.060 |
0.010 |
3.788 |
| SMC |
4.0 |
0.045 |
0.043 |
0.008 |
0.316 |
| SMC |
10.0 |
0.031 |
0.031 |
0.008 |
0.060 |
| SMC |
50.0 |
0.028 |
0.029 |
0.008 |
-0.143 |
| Metro |
2.1 |
0.319 |
0.118 |
0.039 |
5.107 |
| Metro |
3.0 |
0.266 |
0.060 |
0.010 |
20.043 |
| Metro |
4.0 |
0.192 |
0.043 |
0.008 |
18.835 |
| Metro |
10.0 |
0.114 |
0.031 |
0.008 |
10.357 |
| Metro |
50.0 |
0.085 |
0.029 |
0.008 |
6.646 |
| DEMetro_Z |
2.1 |
0.253 |
0.118 |
0.039 |
3.413 |
| DEMetro_Z |
3.0 |
0.147 |
0.060 |
0.010 |
8.499 |
| DEMetro_Z |
4.0 |
0.087 |
0.043 |
0.008 |
5.602 |
| DEMetro_Z |
10.0 |
0.064 |
0.031 |
0.008 |
4.177 |
| DEMetro_Z |
50.0 |
0.046 |
0.029 |
0.008 |
1.947 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
4.293 |
8.73e-05 |
1.538 |
| HMC |
3.0 |
3.764 |
0.000468 |
1.368 |
| HMC |
4.0 |
5.793 |
1.11e-06 |
2.882 |
| HMC |
10.0 |
3.731 |
0.000562 |
1.536 |
| HMC |
50.0 |
3.830 |
0.000344 |
1.207 |
| SMC |
2.1 |
16.001 |
4.16e-16 |
29.239 |
| SMC |
3.0 |
4.532 |
6.81e-05 |
2.868 |
| SMC |
4.0 |
0.342 |
0.733 |
0.100 |
| SMC |
10.0 |
0.051 |
0.959 |
0.014 |
| SMC |
50.0 |
-0.562 |
0.576 |
-0.145 |
| Metro |
2.1 |
8.373 |
2.19e-09 |
10.127 |
| Metro |
3.0 |
10.259 |
1.53e-11 |
9.506 |
| Metro |
4.0 |
10.407 |
1.66e-11 |
13.385 |
| Metro |
10.0 |
8.028 |
4.62e-09 |
8.094 |
| Metro |
50.0 |
7.357 |
2.26e-08 |
5.975 |
| DEMetro_Z |
2.1 |
8.094 |
2.49e-09 |
5.893 |
| DEMetro_Z |
3.0 |
7.633 |
8.91e-09 |
5.548 |
| DEMetro_Z |
4.0 |
9.447 |
1.03e-11 |
4.297 |
| DEMetro_Z |
10.0 |
5.957 |
7.78e-07 |
3.255 |
| DEMetro_Z |
50.0 |
4.729 |
2.38e-05 |
1.870 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
-11.332
|
3.6e-12
|
-2.069
|
| DEMetro_Z_vs_SMC |
1
|
3.165
|
0.00363
|
0.578
|
| DEMetro_Z_vs_SMC |
2
|
8.208
|
4.75e-09
|
1.499
|
| DEMetro_Z_vs_SMC |
3
|
6.124
|
1.13e-06
|
1.118
|
| DEMetro_Z_vs_SMC |
4
|
6.518
|
3.88e-07
|
1.190
|
| HMC_vs_Metro |
0
|
-7.242
|
5.66e-08
|
-1.322
|
| HMC_vs_Metro |
1
|
-8.902
|
8.62e-10
|
-1.625
|
| HMC_vs_Metro |
2
|
-7.492
|
2.95e-08
|
-1.368
|
| HMC_vs_Metro |
3
|
-6.465
|
4.49e-07
|
-1.180
|
| HMC_vs_Metro |
4
|
-5.746
|
3.2e-06
|
-1.049
|
| Metro_vs_DEMetro_Z |
0
|
3.388
|
0.00204
|
0.619
|
| Metro_vs_DEMetro_Z |
1
|
3.257
|
0.00287
|
0.595
|
| Metro_vs_DEMetro_Z |
2
|
6.235
|
8.38e-07
|
1.138
|
| Metro_vs_DEMetro_Z |
3
|
4.279
|
0.000187
|
0.781
|
| Metro_vs_DEMetro_Z |
4
|
4.900
|
3.35e-05
|
0.895
|
| HMC_vs_SMC |
0
|
-14.581
|
6.96e-15
|
-2.662
|
| HMC_vs_SMC |
1
|
-2.145
|
0.0405
|
-0.392
|
| HMC_vs_SMC |
2
|
4.961
|
2.83e-05
|
0.906
|
| HMC_vs_SMC |
3
|
3.372
|
0.00213
|
0.616
|
| HMC_vs_SMC |
4
|
4.574
|
8.26e-05
|
0.835
|
| Metro_vs_SMC |
0
|
-8.522
|
2.17e-09
|
-1.556
|
| Metro_vs_SMC |
1
|
5.832
|
2.53e-06
|
1.065
|
| Metro_vs_SMC |
2
|
10.639
|
1.59e-11
|
1.942
|
| Metro_vs_SMC |
3
|
7.732
|
1.59e-08
|
1.412
|
| Metro_vs_SMC |
4
|
7.950
|
9.1e-09
|
1.451
|
| HMC_vs_DEMetro_Z |
0
|
-5.837
|
2.49e-06
|
-1.066
|
| HMC_vs_DEMetro_Z |
1
|
-5.103
|
1.91e-05
|
-0.932
|
| HMC_vs_DEMetro_Z |
2
|
-2.310
|
0.0282
|
-0.422
|
| HMC_vs_DEMetro_Z |
3
|
-2.763
|
0.00984
|
-0.504
|
| HMC_vs_DEMetro_Z |
4
|
-1.326
|
0.195
|
-0.242
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.023 |
0.015 |
0.006 |
1.538 |
| HMC |
3.0 |
0.021 |
0.015 |
0.005 |
1.368 |
| HMC |
4.0 |
0.023 |
0.013 |
0.004 |
2.882 |
| HMC |
10.0 |
0.021 |
0.014 |
0.005 |
1.536 |
| HMC |
50.0 |
0.021 |
0.015 |
0.005 |
1.207 |
| SMC |
2.1 |
0.177 |
0.015 |
0.006 |
29.239 |
| SMC |
3.0 |
0.028 |
0.015 |
0.005 |
2.868 |
| SMC |
4.0 |
0.013 |
0.013 |
0.004 |
0.100 |
| SMC |
10.0 |
0.014 |
0.014 |
0.005 |
0.014 |
| SMC |
50.0 |
0.014 |
0.015 |
0.005 |
-0.145 |
| Metro |
2.1 |
0.071 |
0.015 |
0.006 |
10.127 |
| Metro |
3.0 |
0.059 |
0.015 |
0.005 |
9.506 |
| Metro |
4.0 |
0.060 |
0.013 |
0.004 |
13.385 |
| Metro |
10.0 |
0.053 |
0.014 |
0.005 |
8.094 |
| Metro |
50.0 |
0.045 |
0.015 |
0.005 |
5.975 |
| DEMetro_Z |
2.1 |
0.047 |
0.015 |
0.006 |
5.893 |
| DEMetro_Z |
3.0 |
0.041 |
0.015 |
0.005 |
5.548 |
| DEMetro_Z |
4.0 |
0.028 |
0.013 |
0.004 |
4.297 |
| DEMetro_Z |
10.0 |
0.029 |
0.014 |
0.005 |
3.255 |
| DEMetro_Z |
50.0 |
0.024 |
0.015 |
0.005 |
1.870 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
0.341 |
0.734 |
0.099 |
| HMC |
3.0 |
4.887 |
2.01e-05 |
2.560 |
| HMC |
4.0 |
2.666 |
0.0112 |
1.331 |
| HMC |
10.0 |
2.225 |
0.0306 |
0.740 |
| HMC |
50.0 |
1.805 |
0.0771 |
0.598 |
| SMC |
2.1 |
3.260 |
0.00196 |
1.028 |
| SMC |
3.0 |
1.362 |
0.18 |
0.491 |
| SMC |
4.0 |
1.611 |
0.113 |
0.449 |
| SMC |
10.0 |
0.331 |
0.742 |
0.089 |
| SMC |
50.0 |
-1.217 |
0.228 |
-0.330 |
| Metro |
2.1 |
6.004 |
1.18e-06 |
5.684 |
| Metro |
3.0 |
6.578 |
2.78e-07 |
8.938 |
| Metro |
4.0 |
6.007 |
1.4e-06 |
9.391 |
| Metro |
10.0 |
4.930 |
2.64e-05 |
4.996 |
| Metro |
50.0 |
5.539 |
4.5e-06 |
5.344 |
| DEMetro_Z |
2.1 |
2.122 |
0.0394 |
0.811 |
| DEMetro_Z |
3.0 |
4.713 |
4.3e-05 |
3.390 |
| DEMetro_Z |
4.0 |
4.073 |
0.000248 |
2.327 |
| DEMetro_Z |
10.0 |
4.350 |
7.75e-05 |
1.658 |
| DEMetro_Z |
50.0 |
3.424 |
0.00143 |
1.531 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-1.793
|
0.0835
|
-0.327
|
| HMC_vs_DEMetro_Z |
1
|
-0.885
|
0.384
|
-0.162
|
| HMC_vs_DEMetro_Z |
2
|
-1.575
|
0.126
|
-0.288
|
| HMC_vs_DEMetro_Z |
3
|
-2.154
|
0.0396
|
-0.393
|
| HMC_vs_DEMetro_Z |
4
|
-2.041
|
0.0504
|
-0.373
|
| Metro_vs_SMC |
0
|
4.859
|
3.75e-05
|
0.887
|
| Metro_vs_SMC |
1
|
6.452
|
4.65e-07
|
1.178
|
| Metro_vs_SMC |
2
|
5.620
|
4.54e-06
|
1.026
|
| Metro_vs_SMC |
3
|
4.827
|
4.1e-05
|
0.881
|
| Metro_vs_SMC |
4
|
5.936
|
1.9e-06
|
1.084
|
| Metro_vs_DEMetro_Z |
0
|
5.261
|
1.23e-05
|
0.961
|
| Metro_vs_DEMetro_Z |
1
|
3.734
|
0.00082
|
0.682
|
| Metro_vs_DEMetro_Z |
2
|
4.385
|
0.00014
|
0.801
|
| Metro_vs_DEMetro_Z |
3
|
3.523
|
0.00143
|
0.643
|
| Metro_vs_DEMetro_Z |
4
|
3.884
|
0.000548
|
0.709
|
| HMC_vs_Metro |
0
|
-5.795
|
2.8e-06
|
-1.058
|
| HMC_vs_Metro |
1
|
-4.349
|
0.000154
|
-0.794
|
| HMC_vs_Metro |
2
|
-5.409
|
8.14e-06
|
-0.988
|
| HMC_vs_Metro |
3
|
-4.516
|
9.72e-05
|
-0.824
|
| HMC_vs_Metro |
4
|
-4.938
|
3.01e-05
|
-0.902
|
| HMC_vs_SMC |
0
|
-2.714
|
0.0111
|
-0.496
|
| HMC_vs_SMC |
1
|
3.714
|
0.000865
|
0.678
|
| HMC_vs_SMC |
2
|
1.814
|
0.0801
|
0.331
|
| HMC_vs_SMC |
3
|
2.036
|
0.0509
|
0.372
|
| HMC_vs_SMC |
4
|
2.606
|
0.0143
|
0.476
|
| DEMetro_Z_vs_SMC |
0
|
-0.476
|
0.638
|
-0.087
|
| DEMetro_Z_vs_SMC |
1
|
3.420
|
0.00188
|
0.624
|
| DEMetro_Z_vs_SMC |
2
|
3.743
|
0.000801
|
0.683
|
| DEMetro_Z_vs_SMC |
3
|
3.674
|
0.000962
|
0.671
|
| DEMetro_Z_vs_SMC |
4
|
4.079
|
0.000323
|
0.745
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.067 |
0.062 |
0.044 |
0.099 |
| HMC |
3.0 |
0.067 |
0.027 |
0.016 |
2.560 |
| HMC |
4.0 |
0.038 |
0.022 |
0.013 |
1.331 |
| HMC |
10.0 |
0.028 |
0.019 |
0.013 |
0.740 |
| HMC |
50.0 |
0.028 |
0.021 |
0.012 |
0.598 |
| SMC |
2.1 |
0.108 |
0.062 |
0.044 |
1.028 |
| SMC |
3.0 |
0.035 |
0.027 |
0.016 |
0.491 |
| SMC |
4.0 |
0.027 |
0.022 |
0.013 |
0.449 |
| SMC |
10.0 |
0.020 |
0.019 |
0.013 |
0.089 |
| SMC |
50.0 |
0.017 |
0.021 |
0.012 |
-0.330 |
| Metro |
2.1 |
0.312 |
0.062 |
0.044 |
5.684 |
| Metro |
3.0 |
0.168 |
0.027 |
0.016 |
8.938 |
| Metro |
4.0 |
0.141 |
0.022 |
0.013 |
9.391 |
| Metro |
10.0 |
0.081 |
0.019 |
0.013 |
4.996 |
| Metro |
50.0 |
0.085 |
0.021 |
0.012 |
5.344 |
| DEMetro_Z |
2.1 |
0.098 |
0.062 |
0.044 |
0.811 |
| DEMetro_Z |
3.0 |
0.081 |
0.027 |
0.016 |
3.390 |
| DEMetro_Z |
4.0 |
0.051 |
0.022 |
0.013 |
2.327 |
| DEMetro_Z |
10.0 |
0.040 |
0.019 |
0.013 |
1.658 |
| DEMetro_Z |
50.0 |
0.039 |
0.021 |
0.012 |
1.531 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
-1.214 |
0.233 |
-0.233 |
| HMC |
3.0 |
1.267 |
0.215 |
2.130 |
| HMC |
4.0 |
1.883 |
0.065 |
0.544 |
| HMC |
10.0 |
3.068 |
0.00385 |
1.371 |
| HMC |
50.0 |
4.798 |
2.27e-05 |
2.180 |
| SMC |
2.1 |
0.318 |
0.752 |
0.066 |
| SMC |
3.0 |
2.664 |
0.0102 |
0.821 |
| SMC |
4.0 |
-0.160 |
0.873 |
-0.040 |
| SMC |
10.0 |
1.293 |
0.201 |
0.365 |
| SMC |
50.0 |
0.412 |
0.682 |
0.117 |
| Metro |
2.1 |
-1.347 |
0.187 |
-0.254 |
| Metro |
3.0 |
2.665 |
0.0103 |
0.865 |
| Metro |
4.0 |
5.177 |
1.15e-05 |
4.040 |
| Metro |
10.0 |
3.946 |
0.000389 |
2.783 |
| Metro |
50.0 |
4.083 |
0.000267 |
2.956 |
| DEMetro_Z |
2.1 |
-1.201 |
0.238 |
-0.227 |
| DEMetro_Z |
3.0 |
2.733 |
0.00838 |
0.779 |
| DEMetro_Z |
4.0 |
1.971 |
0.056 |
0.961 |
| DEMetro_Z |
10.0 |
2.941 |
0.00525 |
1.190 |
| DEMetro_Z |
50.0 |
2.047 |
0.0461 |
0.712 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
-2.666
|
0.0124
|
-0.487
|
| HMC_vs_SMC |
1
|
0.758
|
0.455
|
0.138
|
| HMC_vs_SMC |
2
|
2.049
|
0.0497
|
0.374
|
| HMC_vs_SMC |
3
|
2.086
|
0.0458
|
0.381
|
| HMC_vs_SMC |
4
|
4.159
|
0.000259
|
0.759
|
| Metro_vs_DEMetro_Z |
0
|
-1.176
|
0.249
|
-0.215
|
| Metro_vs_DEMetro_Z |
1
|
0.347
|
0.731
|
0.063
|
| Metro_vs_DEMetro_Z |
2
|
3.141
|
0.00386
|
0.573
|
| Metro_vs_DEMetro_Z |
3
|
2.139
|
0.041
|
0.390
|
| Metro_vs_DEMetro_Z |
4
|
2.860
|
0.00777
|
0.522
|
| HMC_vs_Metro |
0
|
0.545
|
0.59
|
0.100
|
| HMC_vs_Metro |
1
|
0.778
|
0.443
|
0.142
|
| HMC_vs_Metro |
2
|
-4.331
|
0.000162
|
-0.791
|
| HMC_vs_Metro |
3
|
-1.679
|
0.104
|
-0.306
|
| HMC_vs_Metro |
4
|
-1.065
|
0.296
|
-0.194
|
| HMC_vs_DEMetro_Z |
0
|
-0.145
|
0.885
|
-0.027
|
| HMC_vs_DEMetro_Z |
1
|
0.834
|
0.411
|
0.152
|
| HMC_vs_DEMetro_Z |
2
|
-0.753
|
0.458
|
-0.137
|
| HMC_vs_DEMetro_Z |
3
|
0.328
|
0.745
|
0.060
|
| HMC_vs_DEMetro_Z |
4
|
2.782
|
0.00939
|
0.508
|
| Metro_vs_SMC |
0
|
-2.978
|
0.00581
|
-0.544
|
| Metro_vs_SMC |
1
|
0.109
|
0.914
|
0.020
|
| Metro_vs_SMC |
2
|
5.176
|
1.55e-05
|
0.945
|
| Metro_vs_SMC |
3
|
3.300
|
0.00257
|
0.603
|
| Metro_vs_SMC |
4
|
4.251
|
0.000201
|
0.776
|
| DEMetro_Z_vs_SMC |
0
|
-2.857
|
0.00783
|
-0.522
|
| DEMetro_Z_vs_SMC |
1
|
-0.113
|
0.911
|
-0.021
|
| DEMetro_Z_vs_SMC |
2
|
2.024
|
0.0523
|
0.369
|
| DEMetro_Z_vs_SMC |
3
|
2.071
|
0.0474
|
0.378
|
| DEMetro_Z_vs_SMC |
4
|
1.509
|
0.142
|
0.276
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
4.558 |
7.895 |
14.317 |
-0.233 |
| HMC |
3.0 |
1.081 |
0.368 |
0.335 |
2.130 |
| HMC |
4.0 |
0.194 |
0.147 |
0.088 |
0.544 |
| HMC |
10.0 |
0.082 |
0.045 |
0.027 |
1.371 |
| HMC |
50.0 |
0.063 |
0.028 |
0.016 |
2.180 |
| SMC |
2.1 |
8.845 |
7.895 |
14.317 |
0.066 |
| SMC |
3.0 |
0.643 |
0.368 |
0.335 |
0.821 |
| SMC |
4.0 |
0.143 |
0.147 |
0.088 |
-0.040 |
| SMC |
10.0 |
0.055 |
0.045 |
0.027 |
0.365 |
| SMC |
50.0 |
0.030 |
0.028 |
0.016 |
0.117 |
| Metro |
2.1 |
4.264 |
7.895 |
14.317 |
-0.254 |
| Metro |
3.0 |
0.658 |
0.368 |
0.335 |
0.865 |
| Metro |
4.0 |
0.501 |
0.147 |
0.088 |
4.040 |
| Metro |
10.0 |
0.120 |
0.045 |
0.027 |
2.783 |
| Metro |
50.0 |
0.075 |
0.028 |
0.016 |
2.956 |
| DEMetro_Z |
2.1 |
4.641 |
7.895 |
14.317 |
-0.227 |
| DEMetro_Z |
3.0 |
0.629 |
0.368 |
0.335 |
0.779 |
| DEMetro_Z |
4.0 |
0.231 |
0.147 |
0.088 |
0.961 |
| DEMetro_Z |
10.0 |
0.077 |
0.045 |
0.027 |
1.190 |
| DEMetro_Z |
50.0 |
0.040 |
0.028 |
0.016 |
0.712 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
3.926 |
0.000275 |
1.377 |
| HMC |
3.0 |
6.360 |
2.75e-07 |
3.920 |
| HMC |
4.0 |
3.703 |
0.000718 |
2.107 |
| HMC |
10.0 |
5.111 |
6.05e-06 |
1.886 |
| HMC |
50.0 |
4.124 |
0.000147 |
1.438 |
| SMC |
2.1 |
6.018 |
1.41e-06 |
11.610 |
| SMC |
3.0 |
3.879 |
0.000401 |
1.885 |
| SMC |
4.0 |
0.313 |
0.755 |
0.094 |
| SMC |
10.0 |
1.729 |
0.0891 |
0.452 |
| SMC |
50.0 |
-0.975 |
0.334 |
-0.269 |
| Metro |
2.1 |
9.760 |
3.56e-11 |
7.531 |
| Metro |
3.0 |
10.288 |
2.36e-11 |
14.543 |
| Metro |
4.0 |
10.194 |
3.22e-11 |
16.594 |
| Metro |
10.0 |
6.652 |
2.22e-07 |
8.594 |
| Metro |
50.0 |
6.820 |
1.29e-07 |
7.495 |
| DEMetro_Z |
2.1 |
9.503 |
5.49e-13 |
2.995 |
| DEMetro_Z |
3.0 |
9.218 |
1.14e-10 |
6.481 |
| DEMetro_Z |
4.0 |
9.905 |
8.3e-12 |
5.515 |
| DEMetro_Z |
10.0 |
8.285 |
1.54e-10 |
3.226 |
| DEMetro_Z |
50.0 |
5.712 |
1.05e-06 |
2.408 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
5.959
|
1.78e-06
|
1.088
|
| Metro_vs_DEMetro_Z |
1
|
5.249
|
1.27e-05
|
0.958
|
| Metro_vs_DEMetro_Z |
2
|
6.597
|
3.14e-07
|
1.204
|
| Metro_vs_DEMetro_Z |
3
|
4.279
|
0.000187
|
0.781
|
| Metro_vs_DEMetro_Z |
4
|
4.435
|
0.000122
|
0.810
|
| DEMetro_Z_vs_SMC |
0
|
-4.462
|
0.000113
|
-0.815
|
| DEMetro_Z_vs_SMC |
1
|
6.262
|
7.78e-07
|
1.143
|
| DEMetro_Z_vs_SMC |
2
|
10.561
|
1.89e-11
|
1.928
|
| DEMetro_Z_vs_SMC |
3
|
6.862
|
1.55e-07
|
1.253
|
| DEMetro_Z_vs_SMC |
4
|
5.946
|
1.85e-06
|
1.086
|
| HMC_vs_DEMetro_Z |
0
|
-3.877
|
0.000558
|
-0.708
|
| HMC_vs_DEMetro_Z |
1
|
-2.647
|
0.013
|
-0.483
|
| HMC_vs_DEMetro_Z |
2
|
-4.357
|
0.00015
|
-0.796
|
| HMC_vs_DEMetro_Z |
3
|
-2.845
|
0.00806
|
-0.519
|
| HMC_vs_DEMetro_Z |
4
|
-2.057
|
0.0488
|
-0.376
|
| HMC_vs_Metro |
0
|
-7.442
|
3.35e-08
|
-1.359
|
| HMC_vs_Metro |
1
|
-7.187
|
6.54e-08
|
-1.312
|
| HMC_vs_Metro |
2
|
-9.383
|
2.74e-10
|
-1.713
|
| HMC_vs_Metro |
3
|
-5.347
|
9.68e-06
|
-0.976
|
| HMC_vs_Metro |
4
|
-5.352
|
9.54e-06
|
-0.977
|
| HMC_vs_SMC |
0
|
-5.235
|
1.32e-05
|
-0.956
|
| HMC_vs_SMC |
1
|
2.687
|
0.0118
|
0.491
|
| HMC_vs_SMC |
2
|
3.467
|
0.00166
|
0.633
|
| HMC_vs_SMC |
3
|
3.512
|
0.00148
|
0.641
|
| HMC_vs_SMC |
4
|
4.286
|
0.000183
|
0.783
|
| Metro_vs_SMC |
0
|
-1.791
|
0.0838
|
-0.327
|
| Metro_vs_SMC |
1
|
8.629
|
1.67e-09
|
1.575
|
| Metro_vs_SMC |
2
|
9.845
|
9.4e-11
|
1.797
|
| Metro_vs_SMC |
3
|
6.260
|
7.82e-07
|
1.143
|
| Metro_vs_SMC |
4
|
7.149
|
7.22e-08
|
1.305
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.172 |
0.118 |
0.039 |
1.377 |
| HMC |
3.0 |
0.100 |
0.060 |
0.010 |
3.920 |
| HMC |
4.0 |
0.060 |
0.043 |
0.008 |
2.107 |
| HMC |
10.0 |
0.046 |
0.031 |
0.008 |
1.886 |
| HMC |
50.0 |
0.041 |
0.029 |
0.008 |
1.438 |
| SMC |
2.1 |
0.575 |
0.118 |
0.039 |
11.610 |
| SMC |
3.0 |
0.079 |
0.060 |
0.010 |
1.885 |
| SMC |
4.0 |
0.044 |
0.043 |
0.008 |
0.094 |
| SMC |
10.0 |
0.034 |
0.031 |
0.008 |
0.452 |
| SMC |
50.0 |
0.027 |
0.029 |
0.008 |
-0.269 |
| Metro |
2.1 |
0.415 |
0.118 |
0.039 |
7.531 |
| Metro |
3.0 |
0.209 |
0.060 |
0.010 |
14.543 |
| Metro |
4.0 |
0.174 |
0.043 |
0.008 |
16.594 |
| Metro |
10.0 |
0.100 |
0.031 |
0.008 |
8.594 |
| Metro |
50.0 |
0.092 |
0.029 |
0.008 |
7.495 |
| DEMetro_Z |
2.1 |
0.236 |
0.118 |
0.039 |
2.995 |
| DEMetro_Z |
3.0 |
0.126 |
0.060 |
0.010 |
6.481 |
| DEMetro_Z |
4.0 |
0.086 |
0.043 |
0.008 |
5.515 |
| DEMetro_Z |
10.0 |
0.057 |
0.031 |
0.008 |
3.226 |
| DEMetro_Z |
50.0 |
0.050 |
0.029 |
0.008 |
2.408 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
5.184 |
4.55e-06 |
1.872 |
| HMC |
3.0 |
5.314 |
3.37e-06 |
2.068 |
| HMC |
4.0 |
3.289 |
0.00199 |
1.299 |
| HMC |
10.0 |
4.323 |
7.21e-05 |
1.419 |
| HMC |
50.0 |
4.034 |
0.000217 |
1.595 |
| SMC |
2.1 |
7.918 |
9.09e-09 |
19.116 |
| SMC |
3.0 |
2.994 |
0.00459 |
1.242 |
| SMC |
4.0 |
0.305 |
0.761 |
0.094 |
| SMC |
10.0 |
1.766 |
0.0828 |
0.490 |
| SMC |
50.0 |
-0.754 |
0.454 |
-0.214 |
| Metro |
2.1 |
9.720 |
6.03e-11 |
9.425 |
| Metro |
3.0 |
9.411 |
1.46e-10 |
10.114 |
| Metro |
4.0 |
12.195 |
2.63e-13 |
13.114 |
| Metro |
10.0 |
7.525 |
1.72e-08 |
7.296 |
| Metro |
50.0 |
7.418 |
2.01e-08 |
6.295 |
| DEMetro_Z |
2.1 |
8.868 |
6.48e-11 |
4.122 |
| DEMetro_Z |
3.0 |
7.592 |
3.32e-09 |
3.558 |
| DEMetro_Z |
4.0 |
8.876 |
1.27e-10 |
4.825 |
| DEMetro_Z |
10.0 |
5.921 |
4.93e-07 |
2.424 |
| DEMetro_Z |
50.0 |
4.650 |
3.2e-05 |
1.898 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
-6.254
|
7.96e-07
|
-1.142
|
| DEMetro_Z_vs_SMC |
1
|
5.564
|
5.3e-06
|
1.016
|
| DEMetro_Z_vs_SMC |
2
|
10.077
|
5.54e-11
|
1.840
|
| DEMetro_Z_vs_SMC |
3
|
4.404
|
0.000132
|
0.804
|
| DEMetro_Z_vs_SMC |
4
|
4.557
|
8.67e-05
|
0.832
|
| HMC_vs_Metro |
0
|
-7.950
|
9.1e-09
|
-1.451
|
| HMC_vs_Metro |
1
|
-7.682
|
1.8e-08
|
-1.403
|
| HMC_vs_Metro |
2
|
-10.486
|
2.22e-11
|
-1.915
|
| HMC_vs_Metro |
3
|
-5.965
|
1.76e-06
|
-1.089
|
| HMC_vs_Metro |
4
|
-5.369
|
9.11e-06
|
-0.980
|
| Metro_vs_DEMetro_Z |
0
|
4.687
|
6.06e-05
|
0.856
|
| Metro_vs_DEMetro_Z |
1
|
6.464
|
4.5e-07
|
1.180
|
| Metro_vs_DEMetro_Z |
2
|
7.770
|
1.44e-08
|
1.419
|
| Metro_vs_DEMetro_Z |
3
|
4.925
|
3.13e-05
|
0.899
|
| Metro_vs_DEMetro_Z |
4
|
4.578
|
8.18e-05
|
0.836
|
| HMC_vs_SMC |
0
|
-7.322
|
4.59e-08
|
-1.337
|
| HMC_vs_SMC |
1
|
1.777
|
0.0861
|
0.324
|
| HMC_vs_SMC |
2
|
2.997
|
0.00554
|
0.547
|
| HMC_vs_SMC |
3
|
2.557
|
0.016
|
0.467
|
| HMC_vs_SMC |
4
|
3.916
|
0.000502
|
0.715
|
| Metro_vs_SMC |
0
|
-3.623
|
0.0011
|
-0.661
|
| Metro_vs_SMC |
1
|
8.075
|
6.63e-09
|
1.474
|
| Metro_vs_SMC |
2
|
11.879
|
1.16e-12
|
2.169
|
| Metro_vs_SMC |
3
|
7.148
|
7.23e-08
|
1.305
|
| Metro_vs_SMC |
4
|
7.670
|
1.86e-08
|
1.400
|
| HMC_vs_DEMetro_Z |
0
|
-3.958
|
0.000449
|
-0.723
|
| HMC_vs_DEMetro_Z |
1
|
-2.655
|
0.0128
|
-0.485
|
| HMC_vs_DEMetro_Z |
2
|
-5.794
|
2.81e-06
|
-1.058
|
| HMC_vs_DEMetro_Z |
3
|
-2.160
|
0.0391
|
-0.394
|
| HMC_vs_DEMetro_Z |
4
|
-0.588
|
0.561
|
-0.107
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.025 |
0.015 |
0.006 |
1.872 |
| HMC |
3.0 |
0.024 |
0.015 |
0.005 |
2.068 |
| HMC |
4.0 |
0.017 |
0.013 |
0.004 |
1.299 |
| HMC |
10.0 |
0.021 |
0.014 |
0.005 |
1.419 |
| HMC |
50.0 |
0.023 |
0.015 |
0.005 |
1.595 |
| SMC |
2.1 |
0.121 |
0.015 |
0.006 |
19.116 |
| SMC |
3.0 |
0.020 |
0.015 |
0.005 |
1.242 |
| SMC |
4.0 |
0.013 |
0.013 |
0.004 |
0.094 |
| SMC |
10.0 |
0.016 |
0.014 |
0.005 |
0.490 |
| SMC |
50.0 |
0.014 |
0.015 |
0.005 |
-0.214 |
| Metro |
2.1 |
0.067 |
0.015 |
0.006 |
9.425 |
| Metro |
3.0 |
0.062 |
0.015 |
0.005 |
10.114 |
| Metro |
4.0 |
0.059 |
0.013 |
0.004 |
13.114 |
| Metro |
10.0 |
0.049 |
0.014 |
0.005 |
7.296 |
| Metro |
50.0 |
0.046 |
0.015 |
0.005 |
6.295 |
| DEMetro_Z |
2.1 |
0.038 |
0.015 |
0.006 |
4.122 |
| DEMetro_Z |
3.0 |
0.031 |
0.015 |
0.005 |
3.558 |
| DEMetro_Z |
4.0 |
0.030 |
0.013 |
0.004 |
4.825 |
| DEMetro_Z |
10.0 |
0.025 |
0.014 |
0.005 |
2.424 |
| DEMetro_Z |
50.0 |
0.024 |
0.015 |
0.005 |
1.898 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
KDE + Init Plots
Trace Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain
Vary_Tails_with_high_Multimodality
(Mixture,
nu,
30 runs)
Pooled Chains results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
7.831 |
9.93e-09 |
11.492 |
| HMC |
3.0 |
5.572 |
4.95e-06 |
12.373 |
| HMC |
4.0 |
8.188 |
4.66e-09 |
22.303 |
| HMC |
10.0 |
5.170 |
1.56e-05 |
18.164 |
| HMC |
50.0 |
5.818 |
2.6e-06 |
32.462 |
| SMC |
2.1 |
6.532 |
3.12e-07 |
8.659 |
| SMC |
3.0 |
3.921 |
0.00031 |
1.570 |
| SMC |
4.0 |
1.639 |
0.107 |
0.509 |
| SMC |
10.0 |
0.185 |
0.854 |
0.043 |
| SMC |
50.0 |
1.362 |
0.179 |
0.377 |
| Metro |
2.1 |
6.265 |
2.9e-07 |
3.348 |
| Metro |
3.0 |
7.002 |
7.57e-08 |
7.286 |
| Metro |
4.0 |
6.372 |
5.6e-07 |
19.726 |
| Metro |
10.0 |
4.790 |
4.51e-05 |
19.764 |
| Metro |
50.0 |
5.736 |
3.27e-06 |
34.029 |
| DEMetro_Z |
2.1 |
8.206 |
4.3e-09 |
18.141 |
| DEMetro_Z |
3.0 |
6.392 |
4.94e-07 |
11.036 |
| DEMetro_Z |
4.0 |
8.718 |
1.3e-09 |
33.768 |
| DEMetro_Z |
10.0 |
6.373 |
5.61e-07 |
22.497 |
| DEMetro_Z |
50.0 |
7.023 |
9.93e-08 |
35.491 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-2.192
|
0.0366
|
-0.400
|
| HMC_vs_DEMetro_Z |
1
|
0.529
|
0.601
|
0.097
|
| HMC_vs_DEMetro_Z |
2
|
-2.347
|
0.026
|
-0.429
|
| HMC_vs_DEMetro_Z |
3
|
-0.846
|
0.404
|
-0.154
|
| HMC_vs_DEMetro_Z |
4
|
-0.419
|
0.678
|
-0.077
|
| Metro_vs_SMC |
0
|
-3.648
|
0.00103
|
-0.666
|
| Metro_vs_SMC |
1
|
5.277
|
1.18e-05
|
0.963
|
| Metro_vs_SMC |
2
|
6.098
|
1.22e-06
|
1.113
|
| Metro_vs_SMC |
3
|
4.780
|
4.67e-05
|
0.873
|
| Metro_vs_SMC |
4
|
5.718
|
3.46e-06
|
1.044
|
| Metro_vs_DEMetro_Z |
0
|
-6.745
|
2.11e-07
|
-1.231
|
| Metro_vs_DEMetro_Z |
1
|
-1.844
|
0.0754
|
-0.337
|
| Metro_vs_DEMetro_Z |
2
|
-2.858
|
0.0078
|
-0.522
|
| Metro_vs_DEMetro_Z |
3
|
-0.441
|
0.662
|
-0.081
|
| Metro_vs_DEMetro_Z |
4
|
-0.198
|
0.845
|
-0.036
|
| HMC_vs_Metro |
0
|
5.114
|
1.85e-05
|
0.934
|
| HMC_vs_Metro |
1
|
1.978
|
0.0575
|
0.361
|
| HMC_vs_Metro |
2
|
0.597
|
0.555
|
0.109
|
| HMC_vs_Metro |
3
|
-0.350
|
0.729
|
-0.064
|
| HMC_vs_Metro |
4
|
-0.330
|
0.744
|
-0.060
|
| HMC_vs_SMC |
0
|
1.359
|
0.185
|
0.248
|
| HMC_vs_SMC |
1
|
4.774
|
4.75e-05
|
0.872
|
| HMC_vs_SMC |
2
|
7.818
|
1.27e-08
|
1.427
|
| HMC_vs_SMC |
3
|
5.124
|
1.8e-05
|
0.935
|
| HMC_vs_SMC |
4
|
5.801
|
2.76e-06
|
1.059
|
| DEMetro_Z_vs_SMC |
0
|
3.979
|
0.000423
|
0.727
|
| DEMetro_Z_vs_SMC |
1
|
5.477
|
6.75e-06
|
1.000
|
| DEMetro_Z_vs_SMC |
2
|
8.512
|
2.23e-09
|
1.554
|
| DEMetro_Z_vs_SMC |
3
|
6.343
|
6.24e-07
|
1.158
|
| DEMetro_Z_vs_SMC |
4
|
7.031
|
9.87e-08
|
1.284
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.940 |
0.101 |
0.073 |
11.492 |
| HMC |
3.0 |
1.288 |
0.129 |
0.094 |
12.373 |
| HMC |
4.0 |
1.638 |
0.097 |
0.069 |
22.303 |
| HMC |
10.0 |
1.544 |
0.088 |
0.080 |
18.164 |
| HMC |
50.0 |
2.026 |
0.087 |
0.060 |
32.462 |
| SMC |
2.1 |
0.733 |
0.101 |
0.073 |
8.659 |
| SMC |
3.0 |
0.276 |
0.129 |
0.094 |
1.570 |
| SMC |
4.0 |
0.132 |
0.097 |
0.069 |
0.509 |
| SMC |
10.0 |
0.091 |
0.088 |
0.080 |
0.043 |
| SMC |
50.0 |
0.110 |
0.087 |
0.060 |
0.377 |
| Metro |
2.1 |
0.345 |
0.101 |
0.073 |
3.348 |
| Metro |
3.0 |
0.811 |
0.129 |
0.094 |
7.286 |
| Metro |
4.0 |
1.460 |
0.097 |
0.069 |
19.726 |
| Metro |
10.0 |
1.672 |
0.088 |
0.080 |
19.764 |
| Metro |
50.0 |
2.120 |
0.087 |
0.060 |
34.029 |
| DEMetro_Z |
2.1 |
1.425 |
0.101 |
0.073 |
18.141 |
| DEMetro_Z |
3.0 |
1.163 |
0.129 |
0.094 |
11.036 |
| DEMetro_Z |
4.0 |
2.431 |
0.097 |
0.069 |
33.768 |
| DEMetro_Z |
10.0 |
1.891 |
0.088 |
0.080 |
22.497 |
| DEMetro_Z |
50.0 |
2.207 |
0.087 |
0.060 |
35.491 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
-1.300 |
0.203 |
-0.239 |
| HMC |
3.0 |
2.502 |
0.0166 |
1.159 |
| HMC |
4.0 |
4.034 |
0.000364 |
23.406 |
| HMC |
10.0 |
3.891 |
0.000537 |
39.467 |
| HMC |
50.0 |
4.223 |
0.000218 |
62.604 |
| SMC |
2.1 |
-1.341 |
0.19 |
-0.246 |
| SMC |
3.0 |
-1.497 |
0.145 |
-0.275 |
| SMC |
4.0 |
-0.936 |
0.353 |
-0.232 |
| SMC |
10.0 |
-0.520 |
0.605 |
-0.131 |
| SMC |
50.0 |
-1.769 |
0.0825 |
-0.408 |
| Metro |
2.1 |
-1.357 |
0.185 |
-0.250 |
| Metro |
3.0 |
1.646 |
0.106 |
0.350 |
| Metro |
4.0 |
3.258 |
0.00286 |
22.126 |
| Metro |
10.0 |
3.510 |
0.00148 |
52.079 |
| Metro |
50.0 |
4.257 |
0.000198 |
70.022 |
| DEMetro_Z |
2.1 |
-0.866 |
0.393 |
-0.160 |
| DEMetro_Z |
3.0 |
2.723 |
0.00868 |
0.812 |
| DEMetro_Z |
4.0 |
4.826 |
4.11e-05 |
50.166 |
| DEMetro_Z |
10.0 |
3.883 |
0.000549 |
49.977 |
| DEMetro_Z |
50.0 |
4.758 |
4.97e-05 |
64.169 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
0.275
|
0.786
|
0.050
|
| HMC_vs_SMC |
1
|
3.377
|
0.0021
|
0.617
|
| HMC_vs_SMC |
2
|
4.067
|
0.000334
|
0.742
|
| HMC_vs_SMC |
3
|
3.936
|
0.000476
|
0.719
|
| HMC_vs_SMC |
4
|
4.242
|
0.000207
|
0.775
|
| Metro_vs_DEMetro_Z |
0
|
-4.048
|
0.000351
|
-0.739
|
| Metro_vs_DEMetro_Z |
1
|
-1.643
|
0.111
|
-0.300
|
| Metro_vs_DEMetro_Z |
2
|
-2.212
|
0.035
|
-0.404
|
| Metro_vs_DEMetro_Z |
3
|
0.095
|
0.925
|
0.017
|
| Metro_vs_DEMetro_Z |
4
|
0.288
|
0.776
|
0.053
|
| HMC_vs_Metro |
0
|
0.459
|
0.649
|
0.084
|
| HMC_vs_Metro |
1
|
1.824
|
0.0784
|
0.333
|
| HMC_vs_Metro |
2
|
0.130
|
0.897
|
0.024
|
| HMC_vs_Metro |
3
|
-0.755
|
0.456
|
-0.138
|
| HMC_vs_Metro |
4
|
-0.542
|
0.592
|
-0.099
|
| HMC_vs_DEMetro_Z |
0
|
-2.568
|
0.0157
|
-0.469
|
| HMC_vs_DEMetro_Z |
1
|
0.751
|
0.458
|
0.137
|
| HMC_vs_DEMetro_Z |
2
|
-2.153
|
0.0397
|
-0.393
|
| HMC_vs_DEMetro_Z |
3
|
-0.622
|
0.539
|
-0.114
|
| HMC_vs_DEMetro_Z |
4
|
-0.086
|
0.932
|
-0.016
|
| Metro_vs_SMC |
0
|
-0.159
|
0.875
|
-0.029
|
| Metro_vs_SMC |
1
|
5.432
|
7.63e-06
|
0.992
|
| Metro_vs_SMC |
2
|
3.282
|
0.00269
|
0.599
|
| Metro_vs_SMC |
3
|
3.521
|
0.00144
|
0.643
|
| Metro_vs_SMC |
4
|
4.279
|
0.000187
|
0.781
|
| DEMetro_Z_vs_SMC |
0
|
2.867
|
0.00765
|
0.523
|
| DEMetro_Z_vs_SMC |
1
|
4.546
|
8.95e-05
|
0.830
|
| DEMetro_Z_vs_SMC |
2
|
4.826
|
4.12e-05
|
0.881
|
| DEMetro_Z_vs_SMC |
3
|
3.888
|
0.000542
|
0.710
|
| DEMetro_Z_vs_SMC |
4
|
4.784
|
4.62e-05
|
0.873
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
5.044 |
13.069 |
33.570 |
-0.239 |
| HMC |
3.0 |
4.336 |
1.344 |
2.582 |
1.159 |
| HMC |
4.0 |
5.305 |
0.388 |
0.210 |
23.406 |
| HMC |
10.0 |
6.701 |
0.212 |
0.164 |
39.467 |
| HMC |
50.0 |
10.237 |
0.226 |
0.160 |
62.604 |
| SMC |
2.1 |
4.823 |
13.069 |
33.570 |
-0.246 |
| SMC |
3.0 |
0.633 |
1.344 |
2.582 |
-0.275 |
| SMC |
4.0 |
0.340 |
0.388 |
0.210 |
-0.232 |
| SMC |
10.0 |
0.190 |
0.212 |
0.164 |
-0.131 |
| SMC |
50.0 |
0.161 |
0.226 |
0.160 |
-0.408 |
| Metro |
2.1 |
4.680 |
13.069 |
33.570 |
-0.250 |
| Metro |
3.0 |
2.248 |
1.344 |
2.582 |
0.350 |
| Metro |
4.0 |
5.036 |
0.388 |
0.210 |
22.126 |
| Metro |
10.0 |
8.775 |
0.212 |
0.164 |
52.079 |
| Metro |
50.0 |
11.423 |
0.226 |
0.160 |
70.022 |
| DEMetro_Z |
2.1 |
7.691 |
13.069 |
33.570 |
-0.160 |
| DEMetro_Z |
3.0 |
3.441 |
1.344 |
2.582 |
0.812 |
| DEMetro_Z |
4.0 |
10.926 |
0.388 |
0.210 |
50.166 |
| DEMetro_Z |
10.0 |
8.430 |
0.212 |
0.164 |
49.977 |
| DEMetro_Z |
50.0 |
10.487 |
0.226 |
0.160 |
64.169 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
7.930 |
7.03e-09 |
9.872 |
| HMC |
3.0 |
5.733 |
3.2e-06 |
14.648 |
| HMC |
4.0 |
7.822 |
1.2e-08 |
24.159 |
| HMC |
10.0 |
5.121 |
1.79e-05 |
20.015 |
| HMC |
50.0 |
5.782 |
2.88e-06 |
35.147 |
| SMC |
2.1 |
7.989 |
5.68e-09 |
9.089 |
| SMC |
3.0 |
5.523 |
1.82e-06 |
2.244 |
| SMC |
4.0 |
1.966 |
0.0547 |
0.634 |
| SMC |
10.0 |
0.164 |
0.871 |
0.037 |
| SMC |
50.0 |
1.235 |
0.222 |
0.347 |
| Metro |
2.1 |
7.802 |
1.61e-09 |
3.591 |
| Metro |
3.0 |
7.319 |
3.47e-08 |
8.727 |
| Metro |
4.0 |
6.583 |
3.17e-07 |
21.873 |
| Metro |
10.0 |
4.722 |
5.45e-05 |
21.812 |
| Metro |
50.0 |
5.815 |
2.64e-06 |
37.080 |
| DEMetro_Z |
2.1 |
8.691 |
1.23e-09 |
16.339 |
| DEMetro_Z |
3.0 |
6.606 |
2.83e-07 |
13.292 |
| DEMetro_Z |
4.0 |
9.047 |
5.87e-10 |
36.830 |
| DEMetro_Z |
10.0 |
6.577 |
3.24e-07 |
24.262 |
| DEMetro_Z |
50.0 |
6.949 |
1.21e-07 |
38.621 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-6.819
|
1.73e-07
|
-1.245
|
| Metro_vs_DEMetro_Z |
1
|
-1.975
|
0.0578
|
-0.361
|
| Metro_vs_DEMetro_Z |
2
|
-2.856
|
0.00786
|
-0.521
|
| Metro_vs_DEMetro_Z |
3
|
-0.364
|
0.718
|
-0.067
|
| Metro_vs_DEMetro_Z |
4
|
-0.193
|
0.849
|
-0.035
|
| DEMetro_Z_vs_SMC |
0
|
3.605
|
0.00115
|
0.658
|
| DEMetro_Z_vs_SMC |
1
|
5.415
|
8.01e-06
|
0.989
|
| DEMetro_Z_vs_SMC |
2
|
8.808
|
1.08e-09
|
1.608
|
| DEMetro_Z_vs_SMC |
3
|
6.527
|
3.79e-07
|
1.192
|
| DEMetro_Z_vs_SMC |
4
|
6.955
|
1.21e-07
|
1.270
|
| HMC_vs_DEMetro_Z |
0
|
-2.544
|
0.0166
|
-0.464
|
| HMC_vs_DEMetro_Z |
1
|
0.476
|
0.638
|
0.087
|
| HMC_vs_DEMetro_Z |
2
|
-2.409
|
0.0226
|
-0.440
|
| HMC_vs_DEMetro_Z |
3
|
-0.772
|
0.446
|
-0.141
|
| HMC_vs_DEMetro_Z |
4
|
-0.441
|
0.662
|
-0.081
|
| HMC_vs_Metro |
0
|
4.664
|
6.45e-05
|
0.851
|
| HMC_vs_Metro |
1
|
2.011
|
0.0537
|
0.367
|
| HMC_vs_Metro |
2
|
0.471
|
0.641
|
0.086
|
| HMC_vs_Metro |
3
|
-0.348
|
0.73
|
-0.064
|
| HMC_vs_Metro |
4
|
-0.380
|
0.707
|
-0.069
|
| HMC_vs_SMC |
0
|
0.434
|
0.667
|
0.079
|
| HMC_vs_SMC |
1
|
4.775
|
4.74e-05
|
0.872
|
| HMC_vs_SMC |
2
|
7.487
|
2.98e-08
|
1.367
|
| HMC_vs_SMC |
3
|
5.089
|
1.98e-05
|
0.929
|
| HMC_vs_SMC |
4
|
5.768
|
3.02e-06
|
1.053
|
| Metro_vs_SMC |
0
|
-4.471
|
0.00011
|
-0.816
|
| Metro_vs_SMC |
1
|
5.295
|
1.12e-05
|
0.967
|
| Metro_vs_SMC |
2
|
6.269
|
7.64e-07
|
1.144
|
| Metro_vs_SMC |
3
|
4.723
|
5.47e-05
|
0.862
|
| Metro_vs_SMC |
4
|
5.801
|
2.75e-06
|
1.059
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.919 |
0.179 |
0.075 |
9.872 |
| HMC |
3.0 |
1.170 |
0.156 |
0.069 |
14.648 |
| HMC |
4.0 |
1.480 |
0.118 |
0.056 |
24.159 |
| HMC |
10.0 |
1.437 |
0.101 |
0.067 |
20.015 |
| HMC |
50.0 |
1.843 |
0.099 |
0.050 |
35.147 |
| SMC |
2.1 |
0.860 |
0.179 |
0.075 |
9.089 |
| SMC |
3.0 |
0.311 |
0.156 |
0.069 |
2.244 |
| SMC |
4.0 |
0.153 |
0.118 |
0.056 |
0.634 |
| SMC |
10.0 |
0.103 |
0.101 |
0.067 |
0.037 |
| SMC |
50.0 |
0.116 |
0.099 |
0.050 |
0.347 |
| Metro |
2.1 |
0.448 |
0.179 |
0.075 |
3.591 |
| Metro |
3.0 |
0.760 |
0.156 |
0.069 |
8.727 |
| Metro |
4.0 |
1.351 |
0.118 |
0.056 |
21.873 |
| Metro |
10.0 |
1.557 |
0.101 |
0.067 |
21.812 |
| Metro |
50.0 |
1.939 |
0.099 |
0.050 |
37.080 |
| DEMetro_Z |
2.1 |
1.403 |
0.179 |
0.075 |
16.339 |
| DEMetro_Z |
3.0 |
1.076 |
0.156 |
0.069 |
13.292 |
| DEMetro_Z |
4.0 |
2.195 |
0.118 |
0.056 |
36.830 |
| DEMetro_Z |
10.0 |
1.721 |
0.101 |
0.067 |
24.262 |
| DEMetro_Z |
50.0 |
2.016 |
0.099 |
0.050 |
38.621 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
7.636 |
1.78e-08 |
14.077 |
| HMC |
3.0 |
5.296 |
1.09e-05 |
14.974 |
| HMC |
4.0 |
8.008 |
7.47e-09 |
25.181 |
| HMC |
10.0 |
5.247 |
1.26e-05 |
19.667 |
| HMC |
50.0 |
5.933 |
1.9e-06 |
37.328 |
| SMC |
2.1 |
6.520 |
3.46e-07 |
11.010 |
| SMC |
3.0 |
4.162 |
0.000156 |
1.780 |
| SMC |
4.0 |
1.458 |
0.151 |
0.452 |
| SMC |
10.0 |
0.079 |
0.937 |
0.018 |
| SMC |
50.0 |
1.092 |
0.279 |
0.293 |
| Metro |
2.1 |
6.831 |
6.85e-08 |
4.238 |
| Metro |
3.0 |
6.443 |
3.97e-07 |
8.399 |
| Metro |
4.0 |
6.411 |
5.05e-07 |
21.671 |
| Metro |
10.0 |
4.945 |
2.93e-05 |
21.456 |
| Metro |
50.0 |
5.862 |
2.32e-06 |
38.577 |
| DEMetro_Z |
2.1 |
7.654 |
1.85e-08 |
24.051 |
| DEMetro_Z |
3.0 |
6.107 |
1.12e-06 |
13.219 |
| DEMetro_Z |
4.0 |
8.868 |
9.06e-10 |
37.501 |
| DEMetro_Z |
10.0 |
6.486 |
4.15e-07 |
24.500 |
| DEMetro_Z |
50.0 |
7.227 |
5.81e-08 |
40.164 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
3.987
|
0.000415
|
0.728
|
| DEMetro_Z_vs_SMC |
1
|
5.277
|
1.17e-05
|
0.964
|
| DEMetro_Z_vs_SMC |
2
|
8.684
|
1.46e-09
|
1.586
|
| DEMetro_Z_vs_SMC |
3
|
6.459
|
4.56e-07
|
1.179
|
| DEMetro_Z_vs_SMC |
4
|
7.239
|
5.69e-08
|
1.322
|
| HMC_vs_Metro |
0
|
5.029
|
2.34e-05
|
0.918
|
| HMC_vs_Metro |
1
|
1.983
|
0.0569
|
0.362
|
| HMC_vs_Metro |
2
|
0.717
|
0.479
|
0.131
|
| HMC_vs_Metro |
3
|
-0.372
|
0.713
|
-0.068
|
| HMC_vs_Metro |
4
|
-0.234
|
0.816
|
-0.043
|
| Metro_vs_DEMetro_Z |
0
|
-6.109
|
1.18e-06
|
-1.115
|
| Metro_vs_DEMetro_Z |
1
|
-1.890
|
0.0688
|
-0.345
|
| Metro_vs_DEMetro_Z |
2
|
-2.956
|
0.00613
|
-0.540
|
| Metro_vs_DEMetro_Z |
3
|
-0.465
|
0.645
|
-0.085
|
| Metro_vs_DEMetro_Z |
4
|
-0.193
|
0.848
|
-0.035
|
| HMC_vs_SMC |
0
|
1.145
|
0.262
|
0.209
|
| HMC_vs_SMC |
1
|
4.586
|
8e-05
|
0.837
|
| HMC_vs_SMC |
2
|
7.718
|
1.65e-08
|
1.409
|
| HMC_vs_SMC |
3
|
5.222
|
1.37e-05
|
0.953
|
| HMC_vs_SMC |
4
|
5.925
|
1.96e-06
|
1.082
|
| Metro_vs_SMC |
0
|
-3.572
|
0.00126
|
-0.652
|
| Metro_vs_SMC |
1
|
4.957
|
2.86e-05
|
0.905
|
| Metro_vs_SMC |
2
|
6.170
|
9.99e-07
|
1.127
|
| Metro_vs_SMC |
3
|
4.942
|
2.98e-05
|
0.902
|
| Metro_vs_SMC |
4
|
5.857
|
2.36e-06
|
1.069
|
| HMC_vs_DEMetro_Z |
0
|
-2.404
|
0.0228
|
-0.439
|
| HMC_vs_DEMetro_Z |
1
|
0.561
|
0.579
|
0.102
|
| HMC_vs_DEMetro_Z |
2
|
-2.256
|
0.0318
|
-0.412
|
| HMC_vs_DEMetro_Z |
3
|
-0.884
|
0.384
|
-0.161
|
| HMC_vs_DEMetro_Z |
4
|
-0.347
|
0.731
|
-0.063
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.094 |
0.010 |
0.006 |
14.077 |
| HMC |
3.0 |
0.143 |
0.014 |
0.009 |
14.974 |
| HMC |
4.0 |
0.189 |
0.011 |
0.007 |
25.181 |
| HMC |
10.0 |
0.176 |
0.010 |
0.008 |
19.667 |
| HMC |
50.0 |
0.231 |
0.009 |
0.006 |
37.328 |
| SMC |
2.1 |
0.075 |
0.010 |
0.006 |
11.010 |
| SMC |
3.0 |
0.029 |
0.014 |
0.009 |
1.780 |
| SMC |
4.0 |
0.014 |
0.011 |
0.007 |
0.452 |
| SMC |
10.0 |
0.010 |
0.010 |
0.008 |
0.018 |
| SMC |
50.0 |
0.011 |
0.009 |
0.006 |
0.293 |
| Metro |
2.1 |
0.035 |
0.010 |
0.006 |
4.238 |
| Metro |
3.0 |
0.086 |
0.014 |
0.009 |
8.399 |
| Metro |
4.0 |
0.164 |
0.011 |
0.007 |
21.671 |
| Metro |
10.0 |
0.191 |
0.010 |
0.008 |
21.456 |
| Metro |
50.0 |
0.239 |
0.009 |
0.006 |
38.577 |
| DEMetro_Z |
2.1 |
0.153 |
0.010 |
0.006 |
24.051 |
| DEMetro_Z |
3.0 |
0.128 |
0.014 |
0.009 |
13.219 |
| DEMetro_Z |
4.0 |
0.276 |
0.011 |
0.007 |
37.501 |
| DEMetro_Z |
10.0 |
0.217 |
0.010 |
0.008 |
24.500 |
| DEMetro_Z |
50.0 |
0.248 |
0.009 |
0.006 |
40.164 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
R Hat (scatter)
Mode Transitions
One Chain results
Mean Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
5.901 |
1.86e-06 |
8.655 |
| HMC |
3.0 |
7.185 |
5.8e-08 |
12.725 |
| HMC |
4.0 |
6.372 |
5.65e-07 |
23.935 |
| HMC |
10.0 |
34.424 |
2.22e-25 |
67.200 |
| HMC |
50.0 |
290.319 |
1.55e-84 |
93.216 |
| SMC |
2.1 |
6.815 |
1.49e-07 |
10.083 |
| SMC |
3.0 |
2.860 |
0.00664 |
1.244 |
| SMC |
4.0 |
1.705 |
0.0936 |
0.449 |
| SMC |
10.0 |
0.027 |
0.979 |
0.006 |
| SMC |
50.0 |
1.179 |
0.243 |
0.325 |
| Metro |
2.1 |
4.548 |
6.93e-05 |
3.260 |
| Metro |
3.0 |
4.445 |
0.000107 |
4.899 |
| Metro |
4.0 |
4.544 |
8.95e-05 |
26.049 |
| Metro |
10.0 |
13.097 |
9.94e-14 |
57.467 |
| Metro |
50.0 |
42.159 |
7.31e-28 |
91.118 |
| DEMetro_Z |
2.1 |
5.049 |
2.2e-05 |
23.919 |
| DEMetro_Z |
3.0 |
5.797 |
2.65e-06 |
12.711 |
| DEMetro_Z |
4.0 |
4.873 |
3.59e-05 |
28.312 |
| DEMetro_Z |
10.0 |
11.959 |
9.45e-13 |
56.954 |
| DEMetro_Z |
50.0 |
13.312 |
6.78e-14 |
78.965 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_DEMetro_Z |
0
|
-3.000
|
0.00549
|
-0.548
|
| HMC_vs_DEMetro_Z |
1
|
0.005
|
0.996
|
0.001
|
| HMC_vs_DEMetro_Z |
2
|
-0.687
|
0.497
|
-0.126
|
| HMC_vs_DEMetro_Z |
3
|
1.902
|
0.0672
|
0.347
|
| HMC_vs_DEMetro_Z |
4
|
2.380
|
0.0241
|
0.434
|
| Metro_vs_SMC |
0
|
-4.328
|
0.000163
|
-0.790
|
| Metro_vs_SMC |
1
|
2.832
|
0.00832
|
0.517
|
| Metro_vs_SMC |
2
|
4.505
|
0.0001
|
0.823
|
| Metro_vs_SMC |
3
|
13.228
|
8.19e-14
|
2.415
|
| Metro_vs_SMC |
4
|
42.297
|
1.29e-27
|
7.722
|
| Metro_vs_DEMetro_Z |
0
|
-4.383
|
0.00014
|
-0.800
|
| Metro_vs_DEMetro_Z |
1
|
-3.048
|
0.00487
|
-0.557
|
| Metro_vs_DEMetro_Z |
2
|
-0.309
|
0.759
|
-0.056
|
| Metro_vs_DEMetro_Z |
3
|
0.102
|
0.92
|
0.019
|
| Metro_vs_DEMetro_Z |
4
|
1.859
|
0.0732
|
0.339
|
| HMC_vs_Metro |
0
|
3.243
|
0.00297
|
0.592
|
| HMC_vs_Metro |
1
|
3.456
|
0.00171
|
0.631
|
| HMC_vs_Metro |
2
|
-0.306
|
0.762
|
-0.056
|
| HMC_vs_Metro |
3
|
1.968
|
0.0587
|
0.359
|
| HMC_vs_Metro |
4
|
0.983
|
0.334
|
0.179
|
| HMC_vs_SMC |
0
|
-0.621
|
0.539
|
-0.113
|
| HMC_vs_SMC |
1
|
6.379
|
5.67e-07
|
1.165
|
| HMC_vs_SMC |
2
|
6.148
|
1.06e-06
|
1.122
|
| HMC_vs_SMC |
3
|
33.389
|
1.07e-24
|
6.096
|
| HMC_vs_SMC |
4
|
282.803
|
1.89e-51
|
51.632
|
| DEMetro_Z_vs_SMC |
0
|
2.785
|
0.00934
|
0.508
|
| DEMetro_Z_vs_SMC |
1
|
5.239
|
1.31e-05
|
0.956
|
| DEMetro_Z_vs_SMC |
2
|
4.772
|
4.77e-05
|
0.871
|
| DEMetro_Z_vs_SMC |
3
|
12.041
|
8.35e-13
|
2.198
|
| DEMetro_Z_vs_SMC |
4
|
13.200
|
8.64e-14
|
2.410
|
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.732 |
0.101 |
0.073 |
8.655 |
| HMC |
3.0 |
1.321 |
0.129 |
0.094 |
12.725 |
| HMC |
4.0 |
1.751 |
0.097 |
0.069 |
23.935 |
| HMC |
10.0 |
5.474 |
0.088 |
0.080 |
67.200 |
| HMC |
50.0 |
5.655 |
0.087 |
0.060 |
93.216 |
| SMC |
2.1 |
0.837 |
0.101 |
0.073 |
10.083 |
| SMC |
3.0 |
0.245 |
0.129 |
0.094 |
1.244 |
| SMC |
4.0 |
0.128 |
0.097 |
0.069 |
0.449 |
| SMC |
10.0 |
0.088 |
0.088 |
0.080 |
0.006 |
| SMC |
50.0 |
0.107 |
0.087 |
0.060 |
0.325 |
| Metro |
2.1 |
0.339 |
0.101 |
0.073 |
3.260 |
| Metro |
3.0 |
0.588 |
0.129 |
0.094 |
4.899 |
| Metro |
4.0 |
1.897 |
0.097 |
0.069 |
26.049 |
| Metro |
10.0 |
4.694 |
0.088 |
0.080 |
57.467 |
| Metro |
50.0 |
5.529 |
0.087 |
0.060 |
91.118 |
| DEMetro_Z |
2.1 |
1.846 |
0.101 |
0.073 |
23.919 |
| DEMetro_Z |
3.0 |
1.320 |
0.129 |
0.094 |
12.711 |
| DEMetro_Z |
4.0 |
2.054 |
0.097 |
0.069 |
28.312 |
| DEMetro_Z |
10.0 |
4.653 |
0.088 |
0.080 |
56.954 |
| DEMetro_Z |
50.0 |
4.803 |
0.087 |
0.060 |
78.965 |
Var Rmse
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
-1.083 |
0.287 |
-0.203 |
| HMC |
3.0 |
2.669 |
0.0104 |
0.950 |
| HMC |
4.0 |
3.888 |
0.000541 |
32.777 |
| HMC |
10.0 |
28.164 |
1.26e-22 |
261.622 |
| HMC |
50.0 |
1094.111 |
7.94e-127 |
281.285 |
| SMC |
2.1 |
-1.269 |
0.215 |
-0.233 |
| SMC |
3.0 |
-1.332 |
0.192 |
-0.248 |
| SMC |
4.0 |
-1.521 |
0.134 |
-0.391 |
| SMC |
10.0 |
0.247 |
0.805 |
0.065 |
| SMC |
50.0 |
-0.518 |
0.606 |
-0.122 |
| Metro |
2.1 |
-1.063 |
0.296 |
-0.201 |
| Metro |
3.0 |
0.492 |
0.625 |
0.110 |
| Metro |
4.0 |
3.723 |
0.000845 |
56.002 |
| Metro |
10.0 |
11.343 |
3.5e-12 |
219.119 |
| Metro |
50.0 |
32.687 |
1.89e-24 |
272.878 |
| DEMetro_Z |
2.1 |
0.059 |
0.953 |
0.012 |
| DEMetro_Z |
3.0 |
3.016 |
0.00438 |
1.307 |
| DEMetro_Z |
4.0 |
3.744 |
0.000797 |
59.431 |
| DEMetro_Z |
10.0 |
11.113 |
5.71e-12 |
220.637 |
| DEMetro_Z |
50.0 |
12.440 |
3.75e-13 |
235.729 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| HMC_vs_SMC |
0
|
0.799
|
0.431
|
0.146
|
| HMC_vs_SMC |
1
|
3.772
|
0.00074
|
0.689
|
| HMC_vs_SMC |
2
|
3.947
|
0.000462
|
0.721
|
| HMC_vs_SMC |
3
|
28.156
|
1.3e-22
|
5.141
|
| HMC_vs_SMC |
4
|
1222.400
|
6.96e-70
|
223.179
|
| Metro_vs_DEMetro_Z |
0
|
-2.071
|
0.0474
|
-0.378
|
| Metro_vs_DEMetro_Z |
1
|
-2.966
|
0.00599
|
-0.541
|
| Metro_vs_DEMetro_Z |
2
|
-0.178
|
0.86
|
-0.033
|
| Metro_vs_DEMetro_Z |
3
|
-0.072
|
0.943
|
-0.013
|
| Metro_vs_DEMetro_Z |
4
|
1.742
|
0.0921
|
0.318
|
| HMC_vs_Metro |
0
|
-0.045
|
0.965
|
-0.008
|
| HMC_vs_Metro |
1
|
2.342
|
0.0262
|
0.428
|
| HMC_vs_Metro |
2
|
-1.296
|
0.205
|
-0.237
|
| HMC_vs_Metro |
3
|
1.891
|
0.0686
|
0.345
|
| HMC_vs_Metro |
4
|
1.005
|
0.323
|
0.184
|
| HMC_vs_DEMetro_Z |
0
|
-2.251
|
0.0321
|
-0.411
|
| HMC_vs_DEMetro_Z |
1
|
-0.690
|
0.496
|
-0.126
|
| HMC_vs_DEMetro_Z |
2
|
-1.535
|
0.136
|
-0.280
|
| HMC_vs_DEMetro_Z |
3
|
1.787
|
0.0843
|
0.326
|
| HMC_vs_DEMetro_Z |
4
|
2.404
|
0.0228
|
0.439
|
| Metro_vs_SMC |
0
|
0.661
|
0.514
|
0.121
|
| Metro_vs_SMC |
1
|
2.644
|
0.0131
|
0.483
|
| Metro_vs_SMC |
2
|
3.748
|
0.00079
|
0.684
|
| Metro_vs_SMC |
3
|
11.355
|
3.42e-12
|
2.073
|
| Metro_vs_SMC |
4
|
32.633
|
2.05e-24
|
5.958
|
| DEMetro_Z_vs_SMC |
0
|
2.755
|
0.01
|
0.503
|
| DEMetro_Z_vs_SMC |
1
|
3.958
|
0.000448
|
0.723
|
| DEMetro_Z_vs_SMC |
2
|
3.766
|
0.000753
|
0.688
|
| DEMetro_Z_vs_SMC |
3
|
11.135
|
5.46e-12
|
2.033
|
| DEMetro_Z_vs_SMC |
4
|
12.384
|
4.2e-13
|
2.261
|
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
6.256 |
13.069 |
33.570 |
-0.203 |
| HMC |
3.0 |
3.798 |
1.344 |
2.582 |
0.950 |
| HMC |
4.0 |
7.273 |
0.388 |
0.210 |
32.777 |
| HMC |
10.0 |
43.231 |
0.212 |
0.164 |
261.622 |
| HMC |
50.0 |
45.206 |
0.226 |
0.160 |
281.285 |
| SMC |
2.1 |
5.258 |
13.069 |
33.570 |
-0.233 |
| SMC |
3.0 |
0.705 |
1.344 |
2.582 |
-0.248 |
| SMC |
4.0 |
0.306 |
0.388 |
0.210 |
-0.391 |
| SMC |
10.0 |
0.223 |
0.212 |
0.164 |
0.065 |
| SMC |
50.0 |
0.207 |
0.226 |
0.160 |
-0.122 |
| Metro |
2.1 |
6.326 |
13.069 |
33.570 |
-0.201 |
| Metro |
3.0 |
1.627 |
1.344 |
2.582 |
0.110 |
| Metro |
4.0 |
12.152 |
0.388 |
0.210 |
56.002 |
| Metro |
10.0 |
36.242 |
0.212 |
0.164 |
219.119 |
| Metro |
50.0 |
43.861 |
0.226 |
0.160 |
272.878 |
| DEMetro_Z |
2.1 |
13.467 |
13.069 |
33.570 |
0.012 |
| DEMetro_Z |
3.0 |
4.719 |
1.344 |
2.582 |
1.307 |
| DEMetro_Z |
4.0 |
12.872 |
0.388 |
0.210 |
59.431 |
| DEMetro_Z |
10.0 |
36.492 |
0.212 |
0.164 |
220.637 |
| DEMetro_Z |
50.0 |
37.921 |
0.226 |
0.160 |
235.729 |
Wasserstein Distance
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
6.166 |
8.48e-07 |
7.728 |
| HMC |
3.0 |
7.511 |
2.52e-08 |
15.127 |
| HMC |
4.0 |
6.396 |
5.31e-07 |
26.106 |
| HMC |
10.0 |
31.142 |
4.67e-24 |
70.156 |
| HMC |
50.0 |
69.595 |
1.27e-34 |
103.704 |
| SMC |
2.1 |
7.944 |
6.86e-09 |
10.083 |
| SMC |
3.0 |
3.417 |
0.00154 |
1.749 |
| SMC |
4.0 |
1.819 |
0.0741 |
0.469 |
| SMC |
10.0 |
0.224 |
0.824 |
0.053 |
| SMC |
50.0 |
0.695 |
0.49 |
0.183 |
| Metro |
2.1 |
5.177 |
1.07e-05 |
3.593 |
| Metro |
3.0 |
4.721 |
5.07e-05 |
6.167 |
| Metro |
4.0 |
4.534 |
9.22e-05 |
28.602 |
| Metro |
10.0 |
12.874 |
1.54e-13 |
61.779 |
| Metro |
50.0 |
36.639 |
5.17e-26 |
97.467 |
| DEMetro_Z |
2.1 |
5.159 |
1.61e-05 |
20.834 |
| DEMetro_Z |
3.0 |
6.026 |
1.43e-06 |
15.524 |
| DEMetro_Z |
4.0 |
4.911 |
3.24e-05 |
32.043 |
| DEMetro_Z |
10.0 |
11.800 |
1.32e-12 |
61.373 |
| DEMetro_Z |
50.0 |
13.266 |
7.43e-14 |
85.583 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| Metro_vs_DEMetro_Z |
0
|
-4.237
|
0.000209
|
-0.774
|
| Metro_vs_DEMetro_Z |
1
|
-3.102
|
0.00426
|
-0.566
|
| Metro_vs_DEMetro_Z |
2
|
-0.423
|
0.675
|
-0.077
|
| Metro_vs_DEMetro_Z |
3
|
0.073
|
0.942
|
0.013
|
| Metro_vs_DEMetro_Z |
4
|
1.664
|
0.107
|
0.304
|
| DEMetro_Z_vs_SMC |
0
|
2.512
|
0.0178
|
0.459
|
| DEMetro_Z_vs_SMC |
1
|
5.377
|
8.91e-06
|
0.982
|
| DEMetro_Z_vs_SMC |
2
|
4.819
|
4.19e-05
|
0.880
|
| DEMetro_Z_vs_SMC |
3
|
11.874
|
1.17e-12
|
2.168
|
| DEMetro_Z_vs_SMC |
4
|
13.176
|
9.04e-14
|
2.406
|
| HMC_vs_DEMetro_Z |
0
|
-3.014
|
0.00531
|
-0.550
|
| HMC_vs_DEMetro_Z |
1
|
-0.118
|
0.907
|
-0.022
|
| HMC_vs_DEMetro_Z |
2
|
-0.826
|
0.415
|
-0.151
|
| HMC_vs_DEMetro_Z |
3
|
1.527
|
0.138
|
0.279
|
| HMC_vs_DEMetro_Z |
4
|
2.530
|
0.0171
|
0.462
|
| HMC_vs_Metro |
0
|
2.792
|
0.00918
|
0.510
|
| HMC_vs_Metro |
1
|
3.356
|
0.00222
|
0.613
|
| HMC_vs_Metro |
2
|
-0.326
|
0.747
|
-0.060
|
| HMC_vs_Metro |
3
|
1.578
|
0.125
|
0.288
|
| HMC_vs_Metro |
4
|
2.286
|
0.0297
|
0.417
|
| HMC_vs_SMC |
0
|
-1.252
|
0.221
|
-0.229
|
| HMC_vs_SMC |
1
|
6.495
|
4.14e-07
|
1.186
|
| HMC_vs_SMC |
2
|
6.191
|
9.43e-07
|
1.130
|
| HMC_vs_SMC |
3
|
30.431
|
1.47e-23
|
5.556
|
| HMC_vs_SMC |
4
|
69.692
|
7.64e-34
|
12.724
|
| Metro_vs_SMC |
0
|
-4.881
|
3.53e-05
|
-0.891
|
| Metro_vs_SMC |
1
|
2.875
|
0.00748
|
0.525
|
| Metro_vs_SMC |
2
|
4.499
|
0.000102
|
0.821
|
| Metro_vs_SMC |
3
|
12.992
|
1.29e-13
|
2.372
|
| Metro_vs_SMC |
4
|
36.595
|
7.98e-26
|
6.681
|
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.758 |
0.179 |
0.075 |
7.728 |
| HMC |
3.0 |
1.203 |
0.156 |
0.069 |
15.127 |
| HMC |
4.0 |
1.590 |
0.118 |
0.056 |
26.106 |
| HMC |
10.0 |
4.784 |
0.101 |
0.067 |
70.156 |
| HMC |
50.0 |
5.245 |
0.099 |
0.050 |
103.704 |
| SMC |
2.1 |
0.935 |
0.179 |
0.075 |
10.083 |
| SMC |
3.0 |
0.277 |
0.156 |
0.069 |
1.749 |
| SMC |
4.0 |
0.144 |
0.118 |
0.056 |
0.469 |
| SMC |
10.0 |
0.105 |
0.101 |
0.067 |
0.053 |
| SMC |
50.0 |
0.108 |
0.099 |
0.050 |
0.183 |
| Metro |
2.1 |
0.449 |
0.179 |
0.075 |
3.593 |
| Metro |
3.0 |
0.583 |
0.156 |
0.069 |
6.167 |
| Metro |
4.0 |
1.731 |
0.118 |
0.056 |
28.602 |
| Metro |
10.0 |
4.225 |
0.101 |
0.067 |
61.779 |
| Metro |
50.0 |
4.936 |
0.099 |
0.050 |
97.467 |
| DEMetro_Z |
2.1 |
1.740 |
0.179 |
0.075 |
20.834 |
| DEMetro_Z |
3.0 |
1.231 |
0.156 |
0.069 |
15.524 |
| DEMetro_Z |
4.0 |
1.925 |
0.118 |
0.056 |
32.043 |
| DEMetro_Z |
10.0 |
4.198 |
0.101 |
0.067 |
61.373 |
| DEMetro_Z |
50.0 |
4.346 |
0.099 |
0.050 |
85.583 |
Mmd Rff
Sampler vs IID stats
| Sampler |
Varying |
t-stat |
p-value |
Glass Δ |
| HMC |
2.1 |
5.931 |
1.78e-06 |
10.720 |
| HMC |
3.0 |
6.885 |
1.35e-07 |
15.493 |
| HMC |
4.0 |
6.358 |
5.9e-07 |
26.602 |
| HMC |
10.0 |
34.839 |
1.63e-25 |
69.905 |
| HMC |
50.0 |
159.706 |
1.52e-50 |
102.650 |
| SMC |
2.1 |
7.128 |
6.79e-08 |
12.932 |
| SMC |
3.0 |
3.045 |
0.00415 |
1.427 |
| SMC |
4.0 |
1.548 |
0.127 |
0.402 |
| SMC |
10.0 |
0.293 |
0.771 |
0.066 |
| SMC |
50.0 |
0.929 |
0.357 |
0.251 |
| Metro |
2.1 |
4.808 |
3.31e-05 |
3.586 |
| Metro |
3.0 |
4.347 |
0.000145 |
5.830 |
| Metro |
4.0 |
4.490 |
0.000104 |
28.047 |
| Metro |
10.0 |
13.211 |
8.04e-14 |
59.761 |
| Metro |
50.0 |
43.784 |
2.65e-28 |
100.754 |
| DEMetro_Z |
2.1 |
4.882 |
3.51e-05 |
31.682 |
| DEMetro_Z |
3.0 |
5.676 |
3.77e-06 |
15.528 |
| DEMetro_Z |
4.0 |
4.920 |
3.16e-05 |
31.212 |
| DEMetro_Z |
10.0 |
12.068 |
7.6e-13 |
59.925 |
| DEMetro_Z |
50.0 |
13.523 |
4.59e-14 |
86.835 |
Sampler vs Sampler stats
| Sampler Pair |
Varying |
t-stat |
p-value |
Cohen’s d |
| DEMetro_Z_vs_SMC |
0
|
2.756
|
0.01
|
0.503
|
| DEMetro_Z_vs_SMC |
1
|
5.155
|
1.65e-05
|
0.941
|
| DEMetro_Z_vs_SMC |
2
|
4.838
|
3.98e-05
|
0.883
|
| DEMetro_Z_vs_SMC |
3
|
12.142
|
6.8e-13
|
2.217
|
| DEMetro_Z_vs_SMC |
4
|
13.432
|
5.59e-14
|
2.452
|
| HMC_vs_Metro |
0
|
3.567
|
0.00128
|
0.651
|
| HMC_vs_Metro |
1
|
3.336
|
0.00234
|
0.609
|
| HMC_vs_Metro |
2
|
-0.190
|
0.851
|
-0.035
|
| HMC_vs_Metro |
3
|
1.977
|
0.0576
|
0.361
|
| HMC_vs_Metro |
4
|
0.763
|
0.452
|
0.139
|
| Metro_vs_DEMetro_Z |
0
|
-4.410
|
0.00013
|
-0.805
|
| Metro_vs_DEMetro_Z |
1
|
-3.057
|
0.00477
|
-0.558
|
| Metro_vs_DEMetro_Z |
2
|
-0.392
|
0.698
|
-0.072
|
| Metro_vs_DEMetro_Z |
3
|
-0.032
|
0.975
|
-0.006
|
| Metro_vs_DEMetro_Z |
4
|
2.008
|
0.054
|
0.367
|
| HMC_vs_SMC |
0
|
-0.786
|
0.438
|
-0.144
|
| HMC_vs_SMC |
1
|
6.166
|
1.01e-06
|
1.126
|
| HMC_vs_SMC |
2
|
6.172
|
9.94e-07
|
1.127
|
| HMC_vs_SMC |
3
|
33.907
|
6.94e-25
|
6.190
|
| HMC_vs_SMC |
4
|
158.375
|
3.75e-44
|
28.915
|
| Metro_vs_SMC |
0
|
-5.024
|
2.37e-05
|
-0.917
|
| Metro_vs_SMC |
1
|
2.851
|
0.00794
|
0.521
|
| Metro_vs_SMC |
2
|
4.458
|
0.000114
|
0.814
|
| Metro_vs_SMC |
3
|
13.351
|
6.5e-14
|
2.438
|
| Metro_vs_SMC |
4
|
44.028
|
4.1e-28
|
8.038
|
| HMC_vs_DEMetro_Z |
0
|
-3.040
|
0.00498
|
-0.555
|
| HMC_vs_DEMetro_Z |
1
|
-0.010
|
0.992
|
-0.002
|
| HMC_vs_DEMetro_Z |
2
|
-0.666
|
0.511
|
-0.122
|
| HMC_vs_DEMetro_Z |
3
|
1.787
|
0.0844
|
0.326
|
| HMC_vs_DEMetro_Z |
4
|
2.454
|
0.0204
|
0.448
|
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass’s Δ table
| Sampler |
Varying |
MCMC Mean |
IID Mean |
IID Std |
Glass’s Δ |
| HMC |
2.1 |
0.074 |
0.010 |
0.006 |
10.720 |
| HMC |
3.0 |
0.148 |
0.014 |
0.009 |
15.493 |
| HMC |
4.0 |
0.199 |
0.011 |
0.007 |
26.602 |
| HMC |
10.0 |
0.601 |
0.010 |
0.008 |
69.905 |
| HMC |
50.0 |
0.619 |
0.009 |
0.006 |
102.650 |
| SMC |
2.1 |
0.087 |
0.010 |
0.006 |
12.932 |
| SMC |
3.0 |
0.026 |
0.014 |
0.009 |
1.427 |
| SMC |
4.0 |
0.014 |
0.011 |
0.007 |
0.402 |
| SMC |
10.0 |
0.010 |
0.010 |
0.008 |
0.066 |
| SMC |
50.0 |
0.011 |
0.009 |
0.006 |
0.251 |
| Metro |
2.1 |
0.031 |
0.010 |
0.006 |
3.586 |
| Metro |
3.0 |
0.064 |
0.014 |
0.009 |
5.830 |
| Metro |
4.0 |
0.209 |
0.011 |
0.007 |
28.047 |
| Metro |
10.0 |
0.515 |
0.010 |
0.008 |
59.761 |
| Metro |
50.0 |
0.608 |
0.009 |
0.006 |
100.754 |
| DEMetro_Z |
2.1 |
0.198 |
0.010 |
0.006 |
31.682 |
| DEMetro_Z |
3.0 |
0.148 |
0.014 |
0.009 |
15.528 |
| DEMetro_Z |
4.0 |
0.232 |
0.011 |
0.007 |
31.212 |
| DEMetro_Z |
10.0 |
0.517 |
0.010 |
0.008 |
59.925 |
| DEMetro_Z |
50.0 |
0.525 |
0.009 |
0.006 |
86.835 |
Runtime
Runtime (scatter)
Ess
Ess (scatter)
Ess Per Sec
Ess Per Sec (scatter)
R Hat
Mode Transitions
Mode Transitions (scatter)
KDE + Init Plots
Trace Plots
Pooled
Chain
Pairwise Scatter Plots
Pooled
Chain